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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 Homogeneous differential equation ： ウィキペディア英語版 Homogeneous differential equation A differential equation can be homogeneous in either of two respects: the coefficients of the differential terms in the first order case could be homogeneous functions of the variables, or for the linear case of any order there could be no constant term. == Homogeneous type of first-order differential equations == A first-order ordinary differential equation in the form: :$M(x,y)\backslash ,dx\; +\; N(x,y)\backslash ,dy\; =\; 0$ is a homogeneous type if both functions ''M''(''x, y'') and ''N''(''x, y'') are homogeneous functions of the same degree ''n''. That is, multiplying each variable by a parameter  $\backslash lambda$, we find :$M(\backslash lambda\; x,\; \backslash lambda\; y)\; =\; \backslash lambda^n\; M(x,y)\backslash ,$     and     $N(\backslash lambda\; x,\; \backslash lambda\; y)\; =\; \backslash lambda^n\; N(x,y)\backslash ,.$ Thus, :$\backslash frac\; =\; \backslash frac\backslash ,.$ 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「Homogeneous differential 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.