[工數] 注意

[pinwai (我是誰)]

1.利用級數解法求下列微分方程之解

  a. 4(x^2)y"+10xy'+(2-x)y=0

  b. 4xy"+2y'+y=0

  c. y"+y'+(x^2)y=0,  y(0)=1, y'(0)=0  至少寫出前5項

  d. y"-y'+xy=0, y(0)=0, y'(0)=1



2.利用Laplace transform , 求下列積分方程之解

  y(t)=x+積分(從0到x;y(u)cos(x-u)du)



3.利用Laplace transform , 求下列微分方程之解

  y"+2y'+2y=積分(從0到x;f(x-u)(e^u)du)


4.利用Laplace transform , 求下列微分方程組之解

 a.
   x'(t)+y'(t)-x(t)=0
   x'(t)-y'(t)+y(t)=0
   x(0)=1 , y(0)=0

 b.
   x'(t)+x(t)-y(t)=0
   x'(t)-y'(t)+x(t)=0
   x(0)=0 , y(0)=1


5.Find the inverse Laplace transforn of the following function

  a.
        1
  --------------
  ((s^2)+1)(s+1)


  b.
      (s+3)
   ------------e^(3s)
   (s^2)+2s+2

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