Re: [理工] [工數]-ode
※ 引述《smallprawn (水中瑕)》之銘言：
: 應用因變數變更法[即將y(x)換掉.改成v(x)]
: x 2x
: 解 y''+(2e -1)y'+e y=0
: x
: -e x
: A:y=e (c1+c2e )
: 沒頭緒.請高手指教了= =!!
Let y=vu
y'=v'u+vu'
y''=v''u+2v'u'+vu''
->v''u+2v'u'+vu''+(2e^x-1)(v'u+vu')+e^2xuv=0
->uv''+(2u'+(2e^x-1)u)v'+(u''+(2e^x-1)u'+e^2xu)v
pick u=e^(-e^x+(1/2)x)
->v''-1/4v=0
v=c1e^1/2x+c2e^-1/2x
y=e^(-e^x)(c1e^x+c2)
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