Solve the IVP?

y'' - 2y' - 3y = 4*cos(t)*theta(t - pi) with y(0) = y'(0) = 0

use Laplace transformation as easiest path

L(y'') = (s^2)*L(y) - s*y(0) - y'(0); L(y') = s*L(y) - y(0);

L(4*cos(t)*theta(t - pi)) = 4*e^(-pi*s)*L(cos(t + pi)) = -4s*(e^(-pi*s))/((s^2) + 1)

(s^2)*L(y) - 2s*L(y) - 3*L(y) = -4s*(e^(-pi*s))/((s^2) + 1)

L(y) * ((s^2) - 2s - 3) = -4s*(e^(-pi*s))/((s^2) + 1)

L(y) = -4s*(e^(-pi*s))/[((s^2) + 1)*(s - 3)(s + 1)]

y = L^-1{-4s*(e^(-pi*s))/[((s^2) + 1)*(s - 3)(s + 1)]}

y = L^-1[(e^(-pi*s)) * {{4s/[5*((s^2) + 1)]} + {2/[5*((s^2) + 1)]} - {3/[10*(s - 3)]} - {1/[2*(s + 1)]}}]

http://www.wolframalpha.com/input/?i=inverse+lapla...