Re: [理工] [工數]-O.D.E + 拉式
43
y'+y=sinx,y(0)=0
L{y(x)} = Y(s)
sY - y(0) + Y = 1/(s^2+1)
1 1/2 1/2 (1-s)
Y = ___________ (*) = _______(A) + ____________(B)
(s^2+1)(s+1) s+1 s^2 + 1
(A) 用代值法算
(B) 算出(A)之後用(*) - (A) 就好
y(x) = 1/2*exp^(-x) + 1/2*[sinx - cosx]
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