Re: [理工] [工數]-變係數ode
※ 引述《winer8》之銘言：
: xy"+2y'-xy=2e^x
: 答案是C1(1/x)e^x+C2(1/x)e^(-x)+e^x
: 我是用Q-1/4P^2-1/2P'算 到最後出現
: 1/(D^2-1) *2 e^x/(xlnx^-1) 就不會積了
: 另一題是(1-x^2)y"-2y'+2y=0 我怎麼算都不對
: 已知y=x為一解
: 答案是=k1[2+xln[(x-1)/(x+1)]]+k2x
: 真的感謝各位了
xy"+2y'-xy=2e^x
p=2/x Q=-1
1 4 -2
check Q-1/4P^2-1/2P' = -1 - --- ---- - ----- =-1
4 x^2 2x^2
1
則 set u= --- y=uv 帶入 xy"+2y'-xy=2e^x
x
可得 v'' + (-1)v = 2exp(x)
v= c1 exp(x) + c2 exp(-x)+ xexp(x)
ODE通解 y=uv
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