{"id":34421,"date":"2022-04-28T13:00:19","date_gmt":"2022-04-28T13:00:19","guid":{"rendered":"https:\/\/toposuranos.com\/material\/?p=34421"},"modified":"2025-09-08T00:20:24","modified_gmt":"2025-09-08T00:20:24","slug":"%e5%b8%b8%e5%be%ae%e5%88%86%e6%96%b9%e7%a8%8b%e5%bc%8f-edo-%e3%81%a8%e3%81%af%e4%bd%95%e3%81%8b%ef%bc%9f","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/ja\/%e5%b8%b8%e5%be%ae%e5%88%86%e6%96%b9%e7%a8%8b%e5%bc%8f-edo-%e3%81%a8%e3%81%af%e4%bd%95%e3%81%8b%ef%bc%9f\/","title":{"rendered":"\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f (EDO) \u3068\u306f\u4f55\u304b\uff1f"},"content":{"rendered":"<style>\np, ul, ol{\ntext-align: justify;\n}\nh1{\ntext-align:center;\ntext-transform: uppercase;\n}\nh2{\ntext-align:center;\ntext-transform: uppercase;\nfont-size:24pt;\n}\nh3 { \n    text-align: center;\n    text-transform: uppercase;\n    font-size: 24px !important;\n}\n<\/style>\n<h1>\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f (EDO) \u3068\u306f\u4f55\u304b\uff1f<\/h1>\n<p style=\"text-align:center;\" dir=\"ltr\"><em><strong>\u6982\u8981:<\/strong><\/br>\u672c\u8b1b\u7fa9\u3067\u306f\u3001\u968e\u6570 k \u306e\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f (EDO) \u3092\u53d6\u308a\u4e0a\u3052\u3001\u305d\u306e\u5b9a\u7fa9\u3068\u6a19\u6e96\u7684\u304a\u3088\u3073\u4e00\u822c\u7684\u306a\u8868\u73fe\u304b\u3089\u59cb\u3081\u307e\u3059\u3002\u30e4\u30b3\u30d3\u884c\u5217\u3084\u9670\u95a2\u6570\u5b9a\u7406\u3068\u3044\u3063\u305f\u6982\u5ff5\u3092\u901a\u3058\u3066\u3001\u3053\u308c\u3089\u306e\u65b9\u7a0b\u5f0f\u306e\u89e3\u304a\u3088\u3073\u95a2\u9023\u3059\u308b\u6027\u8cea\u3001\u4f8b\u3048\u3070\u5b9a\u7fa9\u57df\u3001\u660e\u793a\u89e3\u304a\u3088\u3073\u9670\u89e3\u306e\u7406\u89e3\u306e\u57fa\u76e4\u3092\u7bc9\u304d\u307e\u3059\u3002<\/em><\/p>\n<p style=\"text-align:center\"><strong>\u5b66\u7fd2\u76ee\u6a19<\/strong><\/p>\n<p>\u672c\u8b1b\u7fa9\u7d42\u4e86\u6642\u3001\u5b66\u751f\u306f\u6b21\u306e\u3053\u3068\u304c\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059\uff1a<\/p>\n<ol>\n<li><strong>\u60f3\u8d77\u3059\u308b<\/strong> \u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f (EDO) \u306e\u5b9a\u7fa9\u3068\u57fa\u672c\u7684\u7279\u5fb4\u3002<\/li>\n<li><strong>\u8aac\u660e\u3059\u308b<\/strong> EDO \u3068\u305d\u306e\u53ef\u80fd\u306a\u89e3\u3068\u306e\u95a2\u4fc2\u3002<\/li>\n<\/ol>\n<p style=\"text-align:center;\" dir=\"ltr\"><strong>\u76ee\u6b21<\/strong><br \/>\n<a href=\"#LaEcuacionDiferencialOrdinariaDeOrdenK\"><strong>\u968e\u6570 k \u306e\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f (EDO)<\/strong><\/a><br \/>\n<a href=\"#TeoremaDeLaFuncionImplicita\">\u9670\u95a2\u6570\u5b9a\u7406<\/a><br \/>\n<a href=\"#LaSolucionDeUnaEcuacionDiferencialOrdinaria\"><strong>\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u89e3<\/strong><\/a><br \/>\n<a href=\"#CuidadoConElDominioDeDefinicionDeLasSoluciones\">\u89e3\u306e\u5b9a\u7fa9\u57df\u306b\u95a2\u3059\u308b\u6ce8\u610f<\/a><br \/>\n<a href=\"#SolucionExtendidaYSolucionMaximal\">\u62e1\u5f35\u89e3\u3068\u6975\u5927\u89e3<\/a><br \/>\n<a href=\"#SolucionExplicitaYSolucionImplicita\">\u660e\u793a\u89e3\u3068\u9670\u89e3<\/a>\n<\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/zE29azRIKng\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/center><\/p>\n<p>\u3053\u3053\u307e\u3067\u306e\u5185\u5bb9\u306b\u3088\u308a\u3001\u5fae\u5206\u65b9\u7a0b\u5f0f\u3068\u306f\u4f55\u304b\u3001\u305d\u3057\u3066\u305d\u308c\u304c\u6301\u3064\u591a\u69d8\u306a\u5fdc\u7528\u306b\u3064\u3044\u3066\u660e\u78ba\u306a\u7406\u89e3\u304c\u5f97\u3089\u308c\u307e\u3057\u305f\u3002\u3053\u3053\u3067\u4e00\u65e6\u7acb\u3061\u6b62\u307e\u308a\u3001\u5171\u901a\u306e\u5f37\u56fa\u306a\u57fa\u76e4\u3092\u7bc9\u304f\u3053\u3068\u3092\u76ee\u7684\u3068\u3057\u3066\u3001\u3044\u304f\u3064\u304b\u306e\u5b9a\u7fa9\u3068\u6027\u8cea\u3092\u691c\u8a0e\u3057\u307e\u3059\u3002<\/p>\n<p><a name=\"LaEcuacionDiferencialOrdinariaDeOrdenK\"><\/a><\/p>\n<h3>\u968e\u6570 k \u306e\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f (EDO)<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=zE29azRIKng&#038;t=163s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #ff0000;\">\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f (EDO)<\/span><\/strong><\/a> \u3068\u306f\u3001\u72ec\u7acb\u5909\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span>\u3001\u95a2\u6570 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y(x)<\/span><\/span>\u3001\u304a\u3088\u3073\u305d\u306e\u3044\u304f\u3064\u304b\u306e\u5e38\u5fae\u5206\u3092\u542b\u3080\u65b9\u7a0b\u5f0f\u306e\u3053\u3068\u3067\u3059\u3002<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y(x)<\/span><\/span> \u306e 1 \u968e\u5e38\u5fae\u5206\u306f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\frac{dy(x)}{dx}<\/span><\/span> \u307e\u305f\u306f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y&#039;(x)<\/span><\/span> \u306e\u3088\u3046\u306a\u8a18\u53f7\u3067\u8868\u3055\u308c\u30012 \u968e\u5e38\u5fae\u5206\u306f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\frac{d^2y(x)}{dx^2}<\/span><\/span> \u307e\u305f\u306f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y&#039;&#039;(x)<\/span><\/span> \u3067\u8868\u3055\u308c\u307e\u3059\u3002\u4e00\u822c\u306b\u3001\u968e\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span> \u306e\u5834\u5408\u306f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\frac{d^ny(x)}{dx^n}<\/span><\/span> \u307e\u305f\u306f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y^{(n)}(x)<\/span><\/span> \u3067\u8868\u3055\u308c\u307e\u3059\u3002\u65b9\u7a0b\u5f0f\u306b\u73fe\u308c\u308b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y^{(k)}(x)<\/span><\/span> \u306e\u968e\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span> \u306e\u6700\u5927\u5024\u3092\u3001\u305d\u306e\u65b9\u7a0b\u5f0f\u306e<strong>\u968e\u6570<\/strong>\u3068\u547c\u3073\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001<strong>\u968e\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span> \u306e EDO \u306e\u4e00\u822c\u5f62<\/strong>\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F\\left(x,y(x),y&#039;(x), \\cdots, y^{(k)}(x)\\right)=0.<\/span>\n<p>\u968e\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span> \u306e EDO \u304c<strong>\u6a19\u6e96\u5f62<\/strong>\u306b\u3042\u308b\u3068\u306f\u3001\u4e0a\u306e\u65b9\u7a0b\u5f0f\u304b\u3089 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y^{(k)}(x)<\/span><\/span> \u3092\u89e3\u304d\u660e\u793a\u7684\u306b\u8868\u3057\u305f\u5834\u5408\u3092\u6307\u3057\u307e\u3059\u3002\u3059\u306a\u308f\u3061\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y^{(k)}(x) = f\\left(x,y(x),y&#039;(x), \\cdots, y^{(k-1)}(x)\\right).<\/span>\n<p>\u4e00\u822c\u306b\u3001\u95a2\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">y<\/span> \u306f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R} \\longrightarrow \\mathbb{R}^n<\/span><\/span> \u306e\u5199\u50cf\u3067\u3042\u308a\u3001\u3053\u306e\u95a2\u6570\u304a\u3088\u3073\u305d\u306e\u5c0e\u95a2\u6570\u306f\u4efb\u610f\u306e\u70b9 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\in\\mathbb{R}<\/span><\/span> \u3067\u8a55\u4fa1\u3055\u308c\u308b\u3068 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R}^n<\/span><\/span> \u306e\u30d9\u30af\u30c8\u30eb\u3068\u306a\u308a\u307e\u3059\u3002\u3053\u306e\u3053\u3068\u3092\u8003\u616e\u3059\u308b\u3068\u3001\u968e\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span> \u306e EDO \u3092\u8a18\u8ff0\u3059\u308b\u95a2\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">F<\/span> \u306b\u306f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">1+(k+1)<\/span><\/span> \u500b\u306e\u5909\u6570\u304c\u542b\u307e\u308c\u308b\u305f\u3081\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\text{Dom}(F)\\subset \\mathbb{R}^{1+n(k+1)}<\/span><\/span> \u304a\u3088\u3073 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\text{Rec}(F)\\subset \\mathbb{R}<\/span><\/span> \u3068\u306a\u308a\u307e\u3059\u3002\u540c\u69d8\u306b\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\text{Dom}(f) = \\mathbb{R}^{1+nk}<\/span><\/span> \u304a\u3088\u3073 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\text{Rec}(f)\\subset \\mathbb{R}^n<\/span><\/span> \u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u968e\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span> \u306e EDO \u306e\u4e00\u822c\u5f62\u304b\u3089\u6a19\u6e96\u5f62\u3078\u306e\u5909\u63db\u306f\u3001<strong>\u9670\u95a2\u6570\u5b9a\u7406<\/strong> \u306b\u3088\u3063\u3066\u53ef\u80fd\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n<p><a name=\"TeoremaDeLaFuncionImplicita\"><\/a><\/p>\n<h4>\u9670\u95a2\u6570\u5b9a\u7406<\/h4>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=zE29azRIKng&#038;t=887s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #ff0000;\"><span class=\"katex-eq\" data-katex-display=\"false\">F<\/span> \u3092\u958b\u96c6\u5408 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">U \\subset \\mathbb{R}^n<\/span><\/span> \u4e0a\u306e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{C}^1<\/span><\/span> \u7d1a\u95a2\u6570\u3068\u3059\u308b<\/span><\/strong><\/a>\u3002\u3055\u3089\u306b\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(a_1,\\cdots, a_n) \\in U<\/span><\/span> \u304c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F(a_1,\\cdots, a_n) = 0<\/span><\/span> \u3092\u6e80\u305f\u3057\u3001<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{\\partial F(a_1,\\cdots, a_n)}{\\partial x_n} \\neq 0<\/span>\n<p>\u3067\u3042\u308b\u3068\u3059\u308b\u3002\u3053\u306e\u3068\u304d\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(a_1, \\cdots, a_{n-1}) \\in \\mathbb{R}^{n-1}<\/span><\/span> \u306e\u8fd1\u508d <span class=\"katex-eq\" data-katex-display=\"false\">V<\/span> \u3068\u3001\u95a2\u6570 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\varphi:V \\longrightarrow \\mathbb{R}<\/span><\/span> \u304c\u5b58\u5728\u3057\u3066\u3001\u6b21\u304c\u6210\u308a\u7acb\u3064\uff1a<\/p>\n<ol>\n<li type=\"i\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">V \\times \\varphi(V) \\subset U<\/span><\/span><\/li>\n<li type=\"i\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F(x_1,\\cdots,x_{n-1},x_n) = 0 \\leftrightarrow x_n = \\varphi(x_1,\\cdots, x_{n-1})<\/span><\/span><\/li>\n<li type=\"i\"><span class=\"katex-eq\" data-katex-display=\"false\">\\varphi<\/span> \u306f\u5fae\u5206\u53ef\u80fd\u3067\u3042\u308a\u3001\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\dfrac{\\partial \\varphi (a_1,\\cdots, a_{n-1})}{\\partial x_i} = - \\dfrac{ \\dfrac{\\partial F (a_1,\\cdots, a_n)}{\\partial x_i} }{ \\dfrac{\\partial F (a_1,\\cdots, a_n)}{\\partial x_n} }<\/span>\n<\/li>\n<\/ol>\n<h4>\u9670\u95a2\u6570\u5b9a\u7406\u306e\u8a3c\u660e<\/h4>\n<h5>\u30e4\u30b3\u30d3\u884c\u5217\u306b\u3088\u308b\u5c55\u958b<\/h5>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=zE29azRIKng&#038;t=1101s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #ff0000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\psi(x_1,\\cdots,x_{n-1}, x_n) = (x_1,\\cdots,x_{n-1}, F(x_1,\\cdots, x_n)).<\/span><\/span> \u3068\u3059\u308b\u3002<\/span><\/strong><\/a> \u305d\u306e\u30e4\u30b3\u30d3\u884c\u5217\u3092\u8a08\u7b97\u3059\u308b\u3068\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\left( \\dfrac{\\partial \\psi(x_1,\\cdots, x_n)}{\\partial(x_1,\\cdots, x_n)} \\right) = \\left( \\begin{array}{cccc}\n\n1 &amp; 0 &amp;  \\cdots &amp; 0 \\\\\n\n0 &amp; 1 &amp;  \\cdots &amp; \\vdots \\\\\n\n\\vdots &amp;\\vdots &amp; \\ddots  &amp; \\vdots  \\\\\n\n\\displaystyle \\dfrac{\\partial F(x_1, \\cdots, x_n)}{\\partial x_1} &amp; \\dfrac{\\partial F(x_1, \\cdots, x_n)}{\\partial x_2} &amp; \\cdots  &amp; \\dfrac{\\partial F(x_1, \\cdots, x_n)}{\\partial x_n}\n\n\\end{array}\\right), <\/span>\n<p>\u3053\u306e\u884c\u5217\u5f0f\u306f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(a_1,\\cdots, a_n)<\/span><\/span> \u306b\u304a\u3044\u3066 0 \u3067\u306f\u306a\u3044\u3053\u3068\u304c\u78ba\u8a8d\u3067\u304d\u307e\u3059\u3002\u3053\u308c\u306f\u5192\u982d\u3067\u8ff0\u3079\u305f\u3088\u3046\u306b\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\partial F(a_1,\\cdots, a_n)\/\\partial x_n \\neq 0<\/span><\/span> \u3067\u3042\u308b\u305f\u3081\u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001<span class=\"katex-eq\" data-katex-display=\"false\">\\psi<\/span> \u306f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(a_1,\\cdots, a_n)<\/span><\/span> \u3092\u542b\u3080\u958b\u96c6\u5408 <span class=\"katex-eq\" data-katex-display=\"false\">W<\/span> \u4e0a\u3067\u9006\u5199\u50cf\u3092\u6301\u3064\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<h5>\u89e3\u306e\u5c55\u958b<\/h5>\n<p>\u3055\u3066\u3001\u96c6\u5408\u3092\u8003\u3048\u308b<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\tilde{V}=\\psi(W)\\ni \\psi(a_1,\\cdots,a_{n}) = (a_1,\\cdots,a_{n-1},F(a_1,\\cdots,a_{n}))=(a_1,\\cdots,a_{n-1},0).<\/span>\n<p>\u3053\u308c\u306b\u57fa\u3065\u304d\u3001\u5225\u306e\u96c6\u5408\u3092\u5b9a\u7fa9\u3067\u304d\u308b<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">V=\\{(x_1,\\cdots,x_{n-1}) \\;|\\; (x_1,\\cdots,x_{n-1},0)\\in \\tilde{V}\\}\\ni (a_1,\\cdots,a_{n-1})<\/span>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u96c6\u5408 <span class=\"katex-eq\" data-katex-display=\"false\">V<\/span> \u306f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(a_1,\\cdots,a_{n-1})\\in\\mathbb{R}^{n-1}<\/span><\/span> \u3092\u542b\u3080\u958b\u96c6\u5408\u3067\u3042\u308b\u3002<\/p>\n<p>\u3055\u3089\u306b\u3001<span class=\"katex-eq\" data-katex-display=\"false\">\\psi<\/span> \u306f\uff08<span class=\"katex-eq\" data-katex-display=\"false\">W<\/span> \u4e0a\u3067\uff09\u9006\u5199\u50cf\u3092\u3082\u3064\u306e\u3067\u3001\u4e00\u610f\u306e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(y_1,\\cdots,y_n)\\in W<\/span><\/span> \u304c\u5b58\u5728\u3057\u3066\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\psi(y_1,\\cdots,y_n) = (x_1,\\cdots,x_{n-1},0)<\/span><\/span> \u3068\u306a\u308b\u3002\u3053\u308c\u306f\u6b21\u3092\u610f\u5473\u3059\u308b\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl} y_1 &amp;= x_1 \\\\ \\\\ \\vdots &amp; \\vdots \\\\ \\\\ y_{n-1} &amp;= x_{n-1} \\\\ \\\\ F(x_1,\\cdots,x_{n-1},y_n) &amp;= 0 \\end{array}<\/span>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\varphi(x_1,\\cdots,x_{n-1}) = y_n<\/span><\/span> \u3068\u5b9a\u7fa9\u3067\u304d\u3001\u6b21\u304c\u6210\u308a\u7acb\u3064\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\psi^{-1}(x_1,\\cdots,x_{n-1},0) = (x_1,\\cdots,x_{n-1},\\varphi(x_1,\\cdots,x_{n-1}))<\/span>\n<p>\u304a\u3088\u3073<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F(x_1,\\cdots,x_{n-1},\\varphi(x_1,\\cdots,x_{n-1})) = 0<\/span>\n<p>\u3053\u308c\u3088\u308a\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\varphi(V)\\ni a_n<\/span><\/span> \u304c\u6210\u308a\u7acb\u3061\u3001\u3057\u305f\u304c\u3063\u3066 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">V\\times\\varphi(V) \\subset U<\/span><\/span> \u3067\u3042\u308a\u3001\u3055\u3089\u306b\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F(x_1,\\cdots,x_{n-1},x_n) = 0 \\leftrightarrow x_n = \\varphi(x_1,\\cdots,x_{n-1})<\/span>\n<h5>\u5fae\u5206\u53ef\u80fd\u6027<\/h5>\n<p>\u6700\u5f8c\u306b\u3001<span class=\"katex-eq\" data-katex-display=\"false\">\\psi<\/span> \u306e\u5fae\u5206\u53ef\u80fd\u6027\u304b\u3089 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\psi^{-1}<\/span><\/span> \u306e\u5fae\u5206\u53ef\u80fd\u6027\u304c\u5c0e\u304b\u308c\u3001\u3055\u3089\u306b <span class=\"katex-eq\" data-katex-display=\"false\">\\varphi<\/span> \u306e <span class=\"katex-eq\" data-katex-display=\"false\">V<\/span> \u4e0a\u3067\u306e\u5fae\u5206\u53ef\u80fd\u6027\u3078\u3068\u5c0e\u304b\u308c\u308b\u3002\u3053\u308c\u3092\u8e0f\u307e\u3048\u3001\u95a2\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">g<\/span> \u3092\u6b21\u306e\u95a2\u4fc2\u3067\u5b9a\u7fa9\u3067\u304d\u308b\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">g(x_1, \\cdots,x_{n-1}) = F(x_1,\\cdots,x_{n-1},\\varphi(x_1,\\cdots,x_{n-1})) = 0<\/span>\n<p>\u6b21\u306b\u3001\u9023\u9396\u5f8b\u3092\u7528\u3044\u308b\u3068\u3001\u6b21\u3092\u5f97\u308b\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{\\partial g}{\\partial x_i} = \\frac{\\partial F}{\\partial x_i} + \\frac{\\partial F}{\\partial x_n}\\frac{\\partial \\varphi }{\\partial x_i} = 0,<\/span>\n<p>\u3053\u3053\u3067\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">i=1,\\cdots, n-1.<\/span><\/span> \u3053\u306e\u6700\u5f8c\u306e\u7b49\u5f0f\u304b\u3089\u6b21\u3092\u5f97\u308b\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\dfrac{\\partial \\varphi(a_1,\\cdots,a_{n-1})}{\\partial x_i} = - \\dfrac{\\dfrac{\\partial F(a_1,\\cdots,a_{n})}{\\partial x_i}}{\\dfrac{\\partial F(a_1,\\cdots,a_{n})}{\\partial x_n}}<\/span>\n<p>\u4ee5\u4e0a\u3067\u793a\u3059\u3079\u304d\u4e8b\u9805\u306f\u3059\u3079\u3066\u8a3c\u660e\u3055\u308c\u305f \u25a0<\/p>\n<p><a name=\"LaSolucionDeUnaEcuacionDiferencialOrdinaria\"><\/a><\/p>\n<h3>\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u89e3<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=zE29azRIKng&#038;t=2249s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #ff0000;\">\u6a19\u6e96\u5f62\u3067\u8868\u3055\u308c\u305f EDO \u3092\u8003\u3048\u308b<\/span><\/strong><\/a><\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y^{(n)} = f(x,y(x),y^\\prime(x),\\cdots,y^{(n-1)(x)})<\/span>\n<p>\u3053\u306e\u3068\u304d\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">I_\\phi<\/span><\/span> \u3092 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R}<\/span><\/span> \u306e\u533a\u9593\u3068\u3059\u308b\u3068\u3001\u95a2\u6570 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\varphi : I_\\phi \\longmapsto \\mathbb{R}^n<\/span><\/span> \u304c<strong>EDO \u306e\u89e3<\/strong>\u3067\u3042\u308b\u3068\u306f\u3001\u6b21\u304c\u6210\u308a\u7acb\u3064\u5834\u5408\u3092\u3044\u3046\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left(\\forall x \\in I_\\phi \\right) \\left(\\varphi^{(n)}(x) = f(x,\\varphi(x),\\varphi^\\prime(x),\\cdots,\\varphi^{(n-1)(x)}\\right)<\/span>\n<p><a name=\"CuidadoConElDominioDeDefinicionDeLasSoluciones\"><\/a><\/p>\n<h4>\u89e3\u306e\u5b9a\u7fa9\u57df\u306b\u95a2\u3059\u308b\u6ce8\u610f<\/h4>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=zE29azRIKng&#038;t=2387s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #ff0000;\">\u3053\u3053\u3067\u5f37\u8abf\u3059\u3079\u304d\u3053\u3068<\/span><\/strong><\/a>\u306f\u3001\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u89e3\u306e\u5b9a\u7fa9\u57df\u3092\u660e\u793a\u7684\u306b\u5ba3\u8a00\u3059\u308b\u91cd\u8981\u6027\u3067\u3042\u308b\u3002\u305f\u3068\u3048\u3070\u3001\u524d\u6bb5\u843d\u3067\u8ff0\u3079\u305f\u95a2\u6570 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\phi<\/span><\/span> \u306e\u5b9a\u7fa9\u57df\u306f\u533a\u9593 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">I_\\phi<\/span><\/span> \u3067\u3042\u308b\u3002\u3053\u308c\u306f\u91cd\u8981\u3067\u3042\u308b\u3002\u306a\u305c\u306a\u3089\u3001\u5fae\u5206\u65b9\u7a0b\u5f0f\u3092\u6271\u3046\u969b\u306e\u4e00\u822c\u7684\u306a\u8aa4\u308a\u306f\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\phi_1<\/span><\/span> \u3068 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\phi_2<\/span><\/span> \u306e\u4e8c\u3064\u306e\u89e3\u304c\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left(\\forall x \\in I_{\\phi_1}\\cap I_{\\phi_2}\\right)\\left(\\phi_1(x) = \\phi_2(x)\\right)<\/span><\/span> \u3092\u6e80\u305f\u3059\u304b\u3089\u3068\u3044\u3063\u3066\u540c\u4e00\u8996\u3057\u3066\u3057\u307e\u3046\u3053\u3068\u3067\u3042\u308b\u3002\u3057\u304b\u3057\u5b9f\u969b\u306b\u306f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">I_{\\phi_1}\\neq I_{\\phi_2}<\/span><\/span> \u3067\u3042\u308b\u5834\u5408\u304c\u3042\u308b\u304b\u3089\u3067\u3042\u308b\u3002\u3053\u306e\u70b9\u3092\u8aac\u660e\u3059\u308b\u305f\u3081\u3001\u6b21\u306e\u5fae\u5206\u65b9\u7a0b\u5f0f\u3092\u8003\u5bdf\u3059\u308b\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y^\\prime = -y^2.<\/span>\n<p>\u3053\u306e EDO \u306e\u4e00\u3064\u306e\u89e3\u306f\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\psi_1 : ]0,+\\infty[ \\longrightarrow \\mathbb{R}^+\\setminus\\{0\\}<\/span><\/span> \u3067\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\psi_1(x)=1\/x<\/span><\/span> \u306b\u3088\u3063\u3066\u5b9a\u7fa9\u3055\u308c\u308b\u3002\u306a\u305c\u306a\u3089\u3001\u4efb\u610f\u306e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\in]0,+\\infty[<\/span><\/span> \u306b\u304a\u3044\u3066 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\psi_1^{\\prime} = -1\/x^2 = -\\psi_1^2<\/span><\/span> \u304c\u6210\u308a\u7acb\u3064\u304b\u3089\u3067\u3042\u308b\u3002\u3057\u304b\u3057\u3001\u5c11\u3057\u4ee3\u6570\u7684\u64cd\u4f5c\u3092\u884c\u3046\u3068\u3001\u7d30\u90e8\u306b\u6ce8\u610f\u3092\u6255\u308f\u306a\u3051\u308c\u3070\u3001\u3053\u308c\u3068\u306f\u5168\u304f\u7570\u306a\u308b\u5225\u306e\u89e3\u306b\u79fb\u3063\u3066\u3057\u307e\u3046\u53ef\u80fd\u6027\u304c\u3042\u308b\u3002\u4f8b\u3048\u3070\u3001\u6b21\u306e\u3053\u3068\u306f\u660e\u3089\u304b\u3067\u3042\u308b\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{1}{x} = \\frac{1}{1 - (1-x)},<\/span>\n<p>\u305d\u3057\u3066\u3001\u3053\u306e\u7b49\u5f0f\u306e\u53f3\u8fba\u306f\u7b49\u6bd4\u7d1a\u6570\u306e\u7d50\u679c\u3067\u3042\u308b\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\displaystyle \\sum_{n=0}^{+\\infty} (1-x)^n = \\frac{1}{1 - (1-x)}<\/span>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u3053\u306e\u3088\u3046\u306a\u6280\u5de7\u306b\u4e0d\u6163\u308c\u306a\u76ee\u306b\u306f\u3001\u95a2\u6570 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\psi_1<\/span><\/span> \u3068 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\psi_2 = \\sum_{n=0}^{+\\infty} (1-x)^n <\/span><\/span> \u304c\u3001\u6700\u521d\u306b\u63d0\u793a\u3055\u308c\u305f\u5fae\u5206\u65b9\u7a0b\u5f0f\u306b\u5bfe\u3057\u3066\u540c\u3058\u89e3\u3092\u4e0e\u3048\u3066\u3044\u308b\u3088\u3046\u306b\u898b\u3048\u308b\u304b\u3082\u3057\u308c\u306a\u3044\u3002\u306a\u305c\u306a\u3089\u3001\u4e21\u8005\u306e\u7d50\u679c\u306f\u5b9f\u969b\u306b\u4e00\u81f4\u3059\u308b\u304b\u3089\u3067\u3042\u308b\u3002\u3057\u304b\u3057\u306a\u304c\u3089\u3001\u3053\u306e\u7b49\u6bd4\u7d1a\u6570\u306f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">|1-x| \\lt 1<\/span><\/span>\u3001\u3059\u306a\u308f\u3061 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\in]0,2[<\/span><\/span> \u306b\u304a\u3044\u3066\u306e\u307f\u6709\u52b9\u3067\u3042\u308b\u3068\u3044\u3046\u70b9\u3092\u898b\u843d\u3068\u3057\u3066\u3044\u308b\u3002\u305d\u3057\u3066\u3055\u3089\u306b\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">]0,2[\\subset]0,+\\infty[<\/span><\/span> \u3067\u3042\u308b\u305f\u3081\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\psi_1<\/span><\/span> \u306f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\psi_2<\/span><\/span> \u3092\u62e1\u5f35\u3057\u3066\u3044\u308b\u3002\u306a\u305c\u306a\u3089\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\psi_2<\/span><\/span> \u304c\u6709\u52b9\u3067\u3042\u308b\u3068\u3053\u308d\u3067\u306f\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\psi_1<\/span><\/span> \u3082\u6709\u52b9\u3067\u3042\u308a\u3001\u304b\u3064\u3055\u3089\u306b\u5e83\u3044\u7bc4\u56f2\u3067\u6210\u308a\u7acb\u3064\u304b\u3089\u3067\u3042\u308b\u3002<\/p>\n<p><a name=\"SolucionExtendidaYSolucionMaximal\"><\/a><\/p>\n<h4>\u62e1\u5f35\u89e3\u3068\u6975\u5927\u89e3<\/h4>\n<p>\u533a\u9593 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">I_{\\phi_1}<\/span><\/span> \u3068 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">I_{\\phi_2}<\/span><\/span> \u4e0a\u3067\u305d\u308c\u305e\u308c\u5b9a\u7fa9\u3055\u308c\u305f\u4e8c\u3064\u306e\u95a2\u6570 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\phi_1<\/span><\/span> \u3068 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\phi_2<\/span><\/span> \u3092\u8003\u3048\u3001\u3053\u308c\u3089\u304c\u3042\u308b\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u89e3\u3067\u3042\u308b\u3068\u3059\u308b\u3002\u3082\u3057 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">I_{\\phi_1}\\subset I_{\\phi_2}<\/span><\/span> \u3067\u3042\u308b\u306a\u3089\u3070\u3001\u89e3 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\phi_2<\/span><\/span> \u306f\u89e3 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\phi_1<\/span><\/span> \u3092\u62e1\u5f35\u3059\u308b\u3068\u8a00\u3044\u3001\u3042\u308b\u3044\u306f\u89e3 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\phi_2<\/span><\/span> \u304c\u89e3 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\phi_1<\/span><\/span> \u3088\u308a\u4e00\u822c\u7684\u3067\u3042\u308b\u3068\u8a00\u3046\u3002\u89e3 <span class=\"katex-eq\" data-katex-display=\"false\">\\phi<\/span> \u304c\u300c\u6975\u5927\u89e3\u300d\u3068\u547c\u3070\u308c\u308b\u306e\u306f\u3001\u305d\u308c\u3092\u975e\u81ea\u660e\u306b\u62e1\u5f35\u3059\u308b\u5225\u306e\u89e3\u304c\u5b58\u5728\u3057\u306a\u3044\u5834\u5408\u3067\u3042\u308b\u3002<\/p>\n<p><a name=\"SolucionExplicitaYSolucionImplicita\"><\/a><\/p>\n<h4>\u660e\u793a\u89e3\u3068\u9670\u89e3<\/h4>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=zE29azRIKng&#038;t=2649s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #ff0000;\">\u95a2\u6570<\/span><\/strong><\/a> <span class=\"katex-eq\" data-katex-display=\"false\">\\phi<\/span> \u304c\u968e\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span> \u306e EDO\uff08\u6a19\u6e96\u5f62\u3067\u66f8\u304b\u308c\u305f\uff09\u306e\u89e3\u3068\u898b\u306a\u3055\u308c\u308b\u306e\u306f\u3001<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y^{(n)}(x)=f(x,y(x),y^\\prime(x),\\cdots,y^{(n-1)}(x)),<\/span>\n<p>\u533a\u9593 <span class=\"katex-eq\" data-katex-display=\"false\">I<\/span> \u306b\u304a\u3044\u3066\u6b21\u304c\u6210\u308a\u7acb\u3064\u3068\u304d\u3067\u3042\u308b\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\forall x\\in I)\\left(\\phi^{n}(x) = f(x,\\phi(x),\\phi^\\prime(x),\\cdots,\\phi^{(n-1)}(x))\\right)<\/span>\n<p>\u3053\u3053\u307e\u3067\u3067\u78ba\u8a8d\u3057\u305f\u5185\u5bb9\u306f\u3001<strong>\u533a\u9593 <span class=\"katex-eq\" data-katex-display=\"false\">I<\/span> \u306b\u304a\u3051\u308b\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u660e\u793a\u89e3<\/strong>\u3068\u3057\u3066\u77e5\u3089\u308c\u3066\u3044\u308b\u3082\u306e\u3067\u3042\u308b\u3002\u305d\u306e\u540d\u304c\u793a\u3059\u3088\u3046\u306b\u3001\u89e3\u3092\u5b9a\u7fa9\u3059\u308b\u3082\u3046\u4e00\u3064\u306e\u65b9\u6cd5\u3068\u3057\u3066\u9670\u7684\u306a\u5f62\u304c\u5b58\u5728\u3059\u308b\u3002\u3059\u306a\u308f\u3061\u3001\u95a2\u4fc2\u5f0f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Phi(x,y)=0<\/span><\/span> \u304c<strong>\u533a\u9593 <span class=\"katex-eq\" data-katex-display=\"false\">I<\/span> \u306b\u304a\u3051\u308b\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u9670\u89e3<\/strong>\u3067\u3042\u308b\u3068\u306f\u3001\u305d\u308c\u304c <span class=\"katex-eq\" data-katex-display=\"false\">I<\/span> \u306b\u304a\u3044\u3066\u4e8c\u3064\u4ee5\u4e0a\u306e\u9670\u7684\u306a\u89e3\u3092\u5b9a\u7fa9\u3059\u308b\u5834\u5408\u3092\u3044\u3046\u3002<\/p>\n<h3>\u7d50\u8ad6<\/h3>\n<p>\u672c\u8b1b\u7fa9\u3067\u306f\u3001\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u6982\u5ff5\u3092\u53b3\u5bc6\u3067\u3042\u308a\u306a\u304c\u3089\u7406\u89e3\u3057\u3084\u3059\u3044\u8996\u70b9\u304b\u3089\u5206\u89e3\u3057\u3001EDO \u3092\u8a8d\u8b58\u3059\u308b\u3060\u3051\u3067\u306a\u304f\u3001\u305d\u306e\u89e3\u306e\u80cc\u5f8c\u306b\u3042\u308b\u8ad6\u7406\u3092\u7406\u89e3\u3059\u308b\u305f\u3081\u306e\u5f62\u5f0f\u7684\u57fa\u76e4\u3092\u78ba\u7acb\u3057\u305f\u3002\u9670\u95a2\u6570\u5b9a\u7406\u306e\u304a\u304b\u3052\u3067\u3001\u4e00\u822c\u5f62\u304b\u3089\u6a19\u6e96\u5f62\u3078\u306e\u79fb\u884c\u3092\u660e\u78ba\u306b\u6b63\u5f53\u5316\u3059\u308b\u3053\u3068\u304c\u53ef\u80fd\u3068\u306a\u308a\u3001\u5177\u4f53\u7684\u306a\u554f\u984c\u306b\u53d6\u308a\u7d44\u3080\u305f\u3081\u306e\u91cd\u8981\u306a\u6280\u8853\u7684\u80fd\u529b\u3078\u3068\u3064\u306a\u304c\u3063\u305f\u3002<\/p>\n<p>\u3055\u3089\u306b\u3001\u89e3\u3092\u7406\u89e3\u3059\u308b\u3055\u307e\u3056\u307e\u306a\u65b9\u6cd5\u3001\u3059\u306a\u308f\u3061\u660e\u793a\u89e3\u3068\u9670\u89e3\u3001\u62e1\u5f35\u89e3\u3068\u6975\u5927\u89e3\u3092\u6b63\u78ba\u306b\u533a\u5225\u3057\u3001\u305d\u306e\u5b9a\u7fa9\u57df\u3092\u9069\u5207\u306b\u5ba3\u8a00\u3059\u308b\u91cd\u8981\u6027\u3092\u5f37\u8abf\u3057\u305f\u3002\u3053\u308c\u3089\u306e\u533a\u5225\u306f\u5358\u306a\u308b\u5f62\u5f0f\u7684\u306a\u3082\u306e\u3067\u306f\u306a\u304f\u3001\u5b9f\u8df5\u7684\u306b\u610f\u5473\u3092\u6301\u3064\u3002\u3053\u308c\u3092\u7121\u8996\u3059\u308b\u3068\u3001\u898b\u305f\u3088\u3046\u306b\u5f97\u3089\u308c\u305f\u7d50\u679c\u306e\u89e3\u91c8\u306b\u304a\u3044\u3066\u6df1\u523b\u306a\u6982\u5ff5\u7684\u8aa4\u308a\u3092\u62db\u304f\u53ef\u80fd\u6027\u304c\u3042\u308b\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f (EDO) \u3068\u306f\u4f55\u304b\uff1f \u6982\u8981:\u672c\u8b1b\u7fa9\u3067\u306f\u3001\u968e\u6570 k \u306e\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f (EDO) \u3092\u53d6\u308a\u4e0a\u3052\u3001\u305d\u306e\u5b9a\u7fa9\u3068\u6a19\u6e96\u7684\u304a\u3088\u3073\u4e00\u822c\u7684\u306a\u8868\u73fe\u304b\u3089\u59cb\u3081\u307e\u3059\u3002\u30e4\u30b3\u30d3\u884c\u5217\u3084\u9670\u95a2\u6570\u5b9a\u7406\u3068\u3044\u3063\u305f\u6982\u5ff5\u3092\u901a\u3058\u3066\u3001\u3053\u308c\u3089\u306e\u65b9\u7a0b\u5f0f\u306e\u89e3\u304a\u3088\u3073\u95a2\u9023\u3059\u308b\u6027\u8cea\u3001\u4f8b\u3048\u3070\u5b9a\u7fa9\u57df\u3001\u660e\u793a\u89e3\u304a\u3088\u3073\u9670\u89e3\u306e\u7406\u89e3\u306e\u57fa\u76e4\u3092\u7bc9\u304d\u307e\u3059\u3002 \u5b66\u7fd2\u76ee\u6a19 \u672c\u8b1b\u7fa9\u7d42\u4e86\u6642\u3001\u5b66\u751f\u306f\u6b21\u306e\u3053\u3068\u304c\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059\uff1a \u60f3\u8d77\u3059\u308b \u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f (EDO) \u306e\u5b9a\u7fa9\u3068\u57fa\u672c\u7684\u7279\u5fb4\u3002 \u8aac\u660e\u3059\u308b EDO \u3068\u305d\u306e\u53ef\u80fd\u306a\u89e3\u3068\u306e\u95a2\u4fc2\u3002 \u76ee\u6b21 \u968e\u6570 k \u306e\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f (EDO) \u9670\u95a2\u6570\u5b9a\u7406 \u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u89e3 \u89e3\u306e\u5b9a\u7fa9\u57df\u306b\u95a2\u3059\u308b\u6ce8\u610f \u62e1\u5f35\u89e3\u3068\u6975\u5927\u89e3 \u660e\u793a\u89e3\u3068\u9670\u89e3 \u3053\u3053\u307e\u3067\u306e\u5185\u5bb9\u306b\u3088\u308a\u3001\u5fae\u5206\u65b9\u7a0b\u5f0f\u3068\u306f\u4f55\u304b\u3001\u305d\u3057\u3066\u305d\u308c\u304c\u6301\u3064\u591a\u69d8\u306a\u5fdc\u7528\u306b\u3064\u3044\u3066\u660e\u78ba\u306a\u7406\u89e3\u304c\u5f97\u3089\u308c\u307e\u3057\u305f\u3002\u3053\u3053\u3067\u4e00\u65e6\u7acb\u3061\u6b62\u307e\u308a\u3001\u5171\u901a\u306e\u5f37\u56fa\u306a\u57fa\u76e4\u3092\u7bc9\u304f\u3053\u3068\u3092\u76ee\u7684\u3068\u3057\u3066\u3001\u3044\u304f\u3064\u304b\u306e\u5b9a\u7fa9\u3068\u6027\u8cea\u3092\u691c\u8a0e\u3057\u307e\u3059\u3002 \u968e\u6570 k \u306e\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f (EDO) \u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f (EDO) \u3068\u306f\u3001\u72ec\u7acb\u5909\u6570 \u3001\u95a2\u6570 \u3001\u304a\u3088\u3073\u305d\u306e\u3044\u304f\u3064\u304b\u306e\u5e38\u5fae\u5206\u3092\u542b\u3080\u65b9\u7a0b\u5f0f\u306e\u3053\u3068\u3067\u3059\u3002 \u306e 1 \u968e\u5e38\u5fae\u5206\u306f \u307e\u305f\u306f \u306e\u3088\u3046\u306a\u8a18\u53f7\u3067\u8868\u3055\u308c\u30012 \u968e\u5e38\u5fae\u5206\u306f \u307e\u305f\u306f \u3067\u8868\u3055\u308c\u307e\u3059\u3002\u4e00\u822c\u306b\u3001\u968e\u6570 \u306e\u5834\u5408\u306f \u307e\u305f\u306f \u3067\u8868\u3055\u308c\u307e\u3059\u3002\u65b9\u7a0b\u5f0f\u306b\u73fe\u308c\u308b \u306e\u968e\u6570 \u306e\u6700\u5927\u5024\u3092\u3001\u305d\u306e\u65b9\u7a0b\u5f0f\u306e\u968e\u6570\u3068\u547c\u3073\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u968e\u6570 \u306e EDO \u306e\u4e00\u822c\u5f62\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\uff1a \u968e\u6570 \u306e [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":32838,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":6,"footnotes":""},"categories":[1199,1350,1300],"tags":[],"class_list":["post-34421","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-sin-categoria-ja","category-1350","category--ja"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f (EDO) \u3068\u306f\u4f55\u304b\uff1f - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u3068\u306f\u4f55\u304b\u3092\u767a\u898b\u3057\u3001\u305d\u306e\u57fa\u790e\u3092\u660e\u78ba\u3055\u3001\u53b3\u5bc6\u3055\u3001\u305d\u3057\u3066\u5177\u4f53\u7684\u306a\u4f8b\u3092\u901a\u3057\u3066\u7fd2\u5f97\u3057\u3088\u3046\u3002\" \/>\n<meta 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