{"id":4837,"date":"2014-02-10T06:00:14","date_gmt":"2014-02-09T21:00:14","guid":{"rendered":"http:\/\/fujiitoshiki.com\/improvesociety\/?p=4837"},"modified":"2014-09-10T16:44:40","modified_gmt":"2014-09-10T07:44:40","slug":"post-4837","status":"publish","type":"post","link":"https:\/\/www.fujiitoshiki.com\/improvesociety\/?p=4837","title":{"rendered":"n<\/em>\u968e\u306e\u4e00\u822c\u7dda\u5f62\u5fae\u5206\u65b9\u7a0b\u5f0f"},"content":{"rendered":"

\u3000n<\/em> \u968e\u306e\u4e00\u822c\u7684\u306a\u7dda\u5f62\u5fae\u5206\u65b9\u7a0b\u5f0f\u306f\u6b21\u306e\u5f62\u3092\u53d6\u308a\u307e\u3059\uff0e<\/p>\n

\\displaystyle a_0(x)\\frac{d^ny}{dx^n} + a_1(x)\\frac{d^{n-1}y}{dx^{n-1}} + \\cdots + a_{n-1}(x)\\frac{dy}{dx} + a_n(x)y = R(x)\\ \\ \\ (1)<\/p>\n

\u3000\u3053\u306e\u5f62\u3067\u66f8\u3051\u306a\u3044\u5fae\u5206\u65b9\u7a0b\u5f0f\u306f\u975e\u7dda\u5f62<\/em>\u3068\u547c\u3070\u308c\u307e\u3059\uff0e<\/p>\n

\\displaystyle x\\frac{d^2y}{dx^2} + 3\\frac{dy}{dx} - 2xy = \\sin x \u306f 2 \u968e\u306e\u7dda\u5f62\u5fae\u5206\u65b9\u7a0b\u5f0f\u3067\u3059\uff0e \\displaystyle y\\frac{d^2y}{dx^2} - x\\left(\\frac{dy}{dx}\\right)^2 + x^2y = e^{-x} \u306f 2 \u968e\u306e\u975e\u7dda\u5f62\u5fae\u5206\u65b9\u7a0b\u5f0f\u3067\u3059\uff0e<\/p>\n

\u3000\u4eee\u306b\u5f0f (1) \u306e\u53f3\u8fba R(x)<\/em> \u3092\u30bc\u30ed\u306b\u7f6e\u63db\u3057\u305f\u5834\u5408\u305d\u306e\u65b9\u7a0b\u5f0f\u306f\u76f8\u88dc<\/em>\uff0c\u7e2e\u7d04<\/em>\u307e\u305f\u306f\u540c\u6b21<\/em>\u65b9\u7a0b\u5f0f\u3068\u547c\u3070\u308c\u307e\u3059\uff0e\u4eee\u306b R(x)<\/em> ≠ 0 \u306e\u6642\uff0c\u305d\u306e\u65b9\u7a0b\u5f0f\u306f \u5b8c\u5168<\/em> \u307e\u305f\u306f \u975e\u540c\u6b21<\/em> \u65b9\u7a0b\u5f0f\u3068\u547c\u3070\u308c\u307e\u3059\uff0e<\/p>\n

\u3000\u4eee\u306b \\displaystyle x\\frac{d^2y}{dx^2} + 3\\frac{dy}{dx} -2xy =\\sin x \u304c\u5b8c\u5168\u65b9\u7a0b\u5f0f\u306e\u6642\uff0c\u3086\u3048\u306b \\displaystyle x\\frac{d^2y}{dx^2} + 3\\frac{dy}{dx} - 2xy = 0 \u306f\u5bfe\u5fdc\u3059\u308b\u76f8\u88dc\uff0c\u7e2e\u7d04\u307e\u305f\u306f\u540c\u6b21\u65b9\u7a0b\u5f0f\u3067\u3059\uff0e<\/p>\n

\u3000\u4eee\u306b a_0(x)\\, \\cdots \\,a_n(x) \u304c\u5168\u3066\u5b9a\u6570\u306e\u6642\uff0c (1) \u306f constant coefficient<\/em> \u3092\u6301\u3064\u3068\u8a00\u308f\u308c\uff0c\u305d\u3046\u3067\u306a\u3051\u308c\u3070 \u5909\u6570\u4fc2\u6570<\/em> \u3092\u6301\u3064\u3068\u8a00\u308f\u308c\u307e\u3059\uff0e<\/p>\n