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- Apr 13, 2013

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I have to find the solution of the equation [tex] y'(x)+5y(x)=e^{-x} , 0<x<\infty , y(0)=2 [/tex] , using the Laplace transform.

That's what I have done so far:

$$L\{y'(x)+5y(x)\}=L\{e^{-x}\}$$

$$L\{y'(x)\}+5L\{y(x)\}=L\{e^{-x}\}$$

$$sY(s)-y(0)+5Y(s)=\frac{1}{s+1}$$

$$Y(s)=\frac{2s+3}{(s+1)(s+5)}$$

But...which are the restrictions for s?How can I find them?