Re: [理工] laplace轉換解微分方程

[Honor1984 (希望願望成真)]

※ 引述《eric820715 (Eric)》之銘言：
: http://i.imgur.com/1dYaVnr.jpg請問這題laplace轉微分方程到這個地方怎麼化簡的呢？
: http://i.imgur.com/xwGuwkK.jpg謝謝～

    1
-------------------
s^2[s^2 + 2s + 2]

         1
= ------------------
   s^2[(s+1)^2 + 1]

   A      B           Ds + E
= ---- + ------  + -------------
   s      s^2       (s+1)^2 + 1


A + D = 0

B = 1/2

5A + 5B + D + E = 1

=> 5A + D + E = -3/2

=> 4A + E = -3/2

-A + B - D + E  = 1

=> -A - D + E = 1/2

=> E = 1/2

=> A = -1/2

=> D = 1/2


    1
-------------------
s^2[s^2 + 2s + 2]

         1
= ------------------
   s^2[(s+1)^2 + 1]

 (-1/2)   1/2        (1/2)[s + 1]
= ---- + ------  + -------------
   s      s^2       (s+1)^2 + 1

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