Step function - laplace

1. Mar 16, 2009

step function - laplace....

1. The problem statement, all variables and given/known data
y"+y = f(t)

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

3. The attempt at a solution

i now have L{y} = $$\frac{1-e^(-(pi/2)s)+s}{s(s^2+1)}$$

but how do i separate them and finish the problem?

thanks

2. Mar 16, 2009

HallsofIvy

Staff Emeritus
Re: step function - laplace....

Use partial fractions like always.
$$\frac{1}{s(s^2+ 1)}= \frac{A}{s}+ \frac{Bs+ C}{s^2+ 1}$$

Find A, B, and C.

3. Mar 16, 2009

so no i have f(t) = 1-cos(t)+sin(t) - L{$$\frac{e^(pi*t/2)}{s(s^2+1)}$$}