I have y"+y=t , y(0)=1, y'=0(adsbygoogle = window.adsbygoogle || []).push({});

After Laplace transformation a got:

(S^3+1)/(S^2(S^2+1))

After I made a partial fraction expansion

(S^3+1)/(S^2(S^2+1))=a1/S^2+a2/S+a3/(S^2+1) (1)

It comes to a system where

a2=1

a1+a3=0 (2)

a2=0

a1=1

Here I am getting confused because according to (1) and (2)

a2 is equal to 0 and 1. What I should use for inverse transformation: zero, one, or both?

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# Homework Help: Laplace transform, fraction expansion

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