[理工] [工數]Laplace解ODE

[paulluo (paulluo)]

Solve the initial value problem by Laplace transformation.

y''+4ty'-4y = 0 ; y(0)=0, y'(0)=5.

  以下是我的算法
sol:
     L{y'} = sY-y(0)  = sY
    L{y''} = s^2 Y - sy(0) - y'(0)
           = s^2 Y - 5
             - d ┌                      ┐
    L{ty'} = ----│s^2 Y - sy(0) - y'(0) │
              ds └                      ┘
              -d ┌         ┐
           = ----│s^2 Y -5 │
              ds └         ┘

           =-sY - s^2 Y'



     s^2 Y - 8s Y - 4s^2 Y' -4sY =0

  => 4s^2 Y'+ (12s-s^2)Y = -5

            (12s-s^2)        -5
  =>  Y' + ----------- Y = ------
               4s^2         4s^2


再來後面解不太出來...

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