推 wichanm :謝了，我發現我v算錯 12/29 19:33
※ 引述《wichanm (wichan)》之銘言：
: Use the method of reduction to find a second solution of the given
: differential equation.
: (x-1)y''-xy'+y = 0 ,x>1 ; y1(x) = exp(x)
: Ans: y2(x) = x
let y=exp(x)*v : y'=exp(x)*v+exp(x)*v'
y"=exp(x)*v+2exp(x)*v'+exp(x)*v" 代入ODE
=> (x-1)v"+(x-2)v'=0 => v=c1xexp(-x)+c2
=> y=exp(x)*v=c1x+c2exp(x) 取c1=1 , c2=0 : y=x為另一獨立解
通解為 y=c3x+c4exp(x)
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※ 編輯: BLUEBL00D 來自: 118.160.38.212 (12/29 18:56)