翻訳と辞書 Words near each other ・ Abel De Los Santos ・ Abel de Pujol ・ Abel Decaux ・ Abel Dhaira ・ Abel Dimier ・ Abel Douay ・ Abel Douglass ・ Abel Dufrane ・ Abel E. Eaton House ・ Abel E. Leavenworth ・ Abel Ebifemowei ・ Abel Echeverría Pineda ・ Abel Ehrlich ・ Abel el'toro ・ Abel equation ・ Abel equation of the first kind ・ Abel Erasmus Pass ・ Abel Ernesto Herrera ・ Abel Estanislao ・ Abel Evans ・ Abel Faivre ・ Abel Fernandez ・ Abel Ferrara ・ Abel Ferreira ・ Abel Ferry ・ Abel Figueiredo ・ Abel Fosdyk papers ・ Abel Foullon ・ Abel François Poisson ・ Abel Fuentes Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Abel equation of the first kind ： ウィキペディア英語版 Abel equation of the first kind In mathematics, an Abel equation of the first kind, named after Niels Henrik Abel, is any ordinary differential equation that is cubic in the unknown function. In other words, it is an equation of the form :$y\text{'}=f\_3(x)y^3+f\_2(x)y^2+f\_1(x)y+f\_0(x)\; \backslash ,$ where $f\_3(x)\backslash neq\; 0$. If $f\_3(x)=0$ and $f\_0(x)=0$, or $f\_2(x)=0$ and $f\_0(x)=0$, the equation reduces to a Bernoulli equation, while if $f\_3(x)\; =\; 0$ the equation reduces to a Riccati equation. ==Properties== The substitution $y=\backslash dfrac$ brings the Abel equation of the first kind to the "Abel equation of the second kind" of the form :$uu\text{'}=-f\_0(x)u^3-f\_1(x)u^2-f\_2(x)u-f\_3(x).\; \backslash ,$ The substitution : $$ \begin \xi & = \int f_3(x)E^2~dx, \\() u & = \left(y+\dfrac\right)E^, \\() E & = \exp\left(\int\left(f_1(x)-\frac\right)~dx\right) \end brings the Abel equation of the first kind to the canonical form :$u\text{'}=u^3+\backslash phi(\backslash xi).\; \backslash ,$ Dimitrios E. Panayotounakos and Theodoros I. Zarmpoutis discovered an analytic method to solve the above equation generally. 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「Abel equation of the first kind」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.