Maths help

[Verdris]

I'm struggling with this and my professor isn't being much of a help.

y''+9y=f(t), , y'(0)=y(0)=0, where

f(t)=sin(pi t) for 0<=t<1 and 0 otherwise.

So I rewrite the RHS as sin(pi t)((u(t)-u(t-1)) = sin(pi t)u(t) - sin(pi t)u(t-1) = sin(pi t)u(t) + sin(pi(t-1))u(t-1)

Taking its Laplace transform, I get (1/s)(pi/(s^2 + pi^2)) + (e^(-s)/s)(pi/(s^2+pi^2)) = (pi/(s^2/pi^2))((1+e^(-s))/s).

Dividing by the transform of the LHS, (pi/(s^2/pi^2))((1+e^(-s))/s)(1/(s^2+9)).

I know I've rewritten f(t) correctly,here's the Wolfram graph: http://www.wolframalpha.com/input/?i...ep%28t-1%29%29

However, my webwork online homework piece of shit tells me I didn't get the transform function correct. What did I miss?

EDIT: found my mistake.

[Remilia]

I'll be honest, I haven't done calculus in years, and the majority of the people on MMO-Champion will probably not be able to answer this.

[Verdris]

I'll be honest, I haven't done calculus in years, and the majority of the people on MMO-Champion will probably not be able to answer this.

figured i'd give it a shot anyway.