Solving Laplace Transform Homework: y''+y = f(t)

[myusernameis]

Homework Statement

y''+y = f(t)

y(0) = 0; y'(0)=1

f(t) = 1, 0<=t<pi/2
0, pi/2<=t

The Attempt at a Solution

so far, i have


(s^2+1)*L{y} = \frac{s-e^(-pi/2s)}{s} +1

what is next ?

 

[gabbagabbahey]

so far, i have (s^2+1)*L{y} = \frac{s-e^(-pi/2s)}{s} +1

what is next ?

That doesn't look quite right; the Laplace Transform of f(t) is not \frac{s-e^{-\pi s/2}}{s} (although it's close). Double check that calculation.

Once you correct your expression, solve for \mathcal{L}[y(t)] and then take the inverse Laplace transform to get y(t)