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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 Bernoulli differential equation ： ウィキペディア英語版 Bernoulli differential equation In mathematics, an ordinary differential equation of the form : $y\text{'}+\; P(x)y\; =\; Q(x)y^n\backslash ,$ is called a Bernoulli equation when n≠1, 0. It is named after Jacob Bernoulli who discussed it in 1695 . Bernoulli equations are special because they are nonlinear differential equations with known exact solutions. A famous special case of the Bernoulli differential equation is the logistic differential equation. ==Solution== Let $x\_0\; \backslash in\; (a,\; b)$ and :$\backslash left\backslash$ z: (a,b) \rightarrow (0, \infty)\ ,&\textrm\ \alpha\in \mathbb\setminus\,\\ z: (a,b) \rightarrow \mathbb\setminus\\ ,&\textrm\ \alpha = 2,\\\end\right. be a solution of the linear differential equation :$z\text{'}(x)=(1-\backslash alpha)P(x)z(x)\; +\; (1-\backslash alpha)Q(x).$ Then we have that $y(x)\; :=\; ()^\}$ is a solution of :$y\text{'}(x)=\; P(x)y(x)\; +\; Q(x)y^\backslash alpha(x)\backslash \; ,\backslash \; y(x\_0)\; =\; y\_0\; :=\; ()^\}.$ And for every such differential equation, for all $\backslash alpha>0$ we have $y\backslash equiv\; 0$ as solution for $y\_0=0$. 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「Bernoulli 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.