Laplace transform of dy/dt = -y + t^2

[ColdFusion85]

This is a Laplace Transform problem. dy/dt = -y + t^2. I formed the inverse laplace transform equation which i verified is correct, then i took partial fraction decompositions and got for a final answer that y = (L inverse) [2/s^3 - 1/(s+1)]. and hence, y = t^2 - e^-t. however the book states that the answer is t^2 - 2*t + 2 - e^-t. where did i go wrong??

 

[ColdFusion85]

Oops, I think it has to be distributed as $$\frac{A}{(s+1)} + \frac{(Bx+C)}{s}+ \frac{(Dx+E)}{(s^2)}+\frac{(Fx+G)}{(s^3)}$$, doesn't it?

 

[ColdFusion85]

nevermind, got it.