Re: [理工] [工數]-ODE
: 2.xy"+2y'-xy=2e^x
: 1
: let y=---u
: x
: y'=-x^-2u+x^-1u'
: y''=2x^-3u-2x^-2u'+x^-1u''
: ->u''-u=2e^x
: ->u=c1e^x+c2e^-2x+xe^x
: ->y=(c1e^x+c2e^-2x+xe^x)/x
請問一下大大如何要找齊性解阿
這題令y=cx^n y'=cnx^(n-1) y"=cn(n-1)x^(n-2)
代入原題目 同除c之後
(n^2 + n)x^(n-1) - x^(n+1) =0
但n=-1帶進去不為0耶??
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