Applying Partial Fractions to Solve Laplace Step Function Problems

[myusernameis]

step function - laplace...

Homework Statement

y"+y = f(t)

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

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

 

[HallsofIvy]

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.

 

[myusernameis]

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.

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

how do i get the last laplace?