Solve:
$$y''+y'+\frac{5}{4}=U_\frac{\pi}{2}(t)f(t-\frac{\pi}{2})$$
becomes:
$$[s^2+s+\frac{5}{4}]Y(s)=\frac{1-e^\frac{-\pi*s}{2}}{s^2}$$
becomes:
$$Y(s)=\frac{1-e^\frac{-\pi*s}{2}}{s^2[(s+\frac{1}{2})^2+1]}$$
and now I am having trouble using the method of partial fractions to move forward. Can anyone help me a bit? I can finish the problem, so I do not need anyone to solve this completely (feel free if you just enjoy solving these types of problems).
The method a friend showed split ^^ that into two and then solved for the $\frac{1}{blah}$ portion. He called this $H(s)$ and then said $Y(s)=H(s)-e^\frac{-\pi*s}{2}H(s)$ and then he finds the inverse Laplace transforms. So maybe I should only decompose the 1/stuff part of that? Any ideas?