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Laplace Transform

1. Homework Statement

y''+y = f(t)

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

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


3. The Attempt at a Solution
so far, i have


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

what is next ?
 

gabbagabbahey

Homework Helper
Gold Member
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so far, i have


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

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

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

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