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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Cauchy–Euler equation ： ウィキペディア英語版 Cauchy–Euler equation In mathematics, a Cauchy–Euler equation (also known as the Euler–Cauchy equation, or simply Euler's equation) is a linear homogeneous ordinary differential equation with variable coefficients. It is sometimes referred to as an ''equidimensional'' equation. Because of the particularly simple equidimensional structure the equation can be replaced with an equivalent equation with constant coefficients which can then be solved explicitly. ==The equation== Let ''y''(''n'')(''x'') be the ''n''th derivative of the unknown function ''y''(''x''). Then a Cauchy–Euler equation of order ''n'' has the form :$a\_\; x^n\; y^(x)\; +\; a\_\; x^\; y^(x)\; +\; \backslash cdots\; +\; a\_0\; y(x)\; =\; 0.$ The substitution $x\; =\; e^u$ reduces this equation to a linear differential equation with constant coefficients. Alternatively a trial solution $y\; =\; x^m$ may be used to solve for the basis solutions. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Cauchy–Euler equation」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.