[理工] [工數] 高階 ODE 幫檢查一下@@

[topee (eason)]

     x^2y" - 3xy' + 4y = 0

另令x=e^t  t =lnx


Dt(Dt-1)y - 3Dty + 4y  = 0

(Dt^2 - 4Dty +4)  y =0


(Dt-2)^2 y  = 0


y = c1 e^2t  +c2 te^2t


  =c1 x^2 + c2(lnx)x^2

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