Laplace transforms

y"(t)+13y'(t)+36y(t)=u(t-2)-u(t-3)
y(0)=0
y'(0)=0
Solve the initial value problem using Laplace transforms.
1)Laplace transform of both sides:
2)solve for Y(s):Y(s)=
3)write out the rational function you apply partial fraction to:
4)write out the partial fraction decomposition:
H(s)=
5)Determine the inverse Laplace transform of H(s) and label it (Ht)
H(t)=
5)write out the solution of initial value problem in terms of unit step functions and H(t).