Solving partial differential equation

Question

Assignment:

Using the method of separation of variables, solve the partial differential equation

u_tt+2(pi)u_t-u_xx=-3sin(3(pi)x)

for 0 less than or equal to x less than or equal to 1 with boundary conditions u(0,t)=u(1,t)=0 and initial conditions u(x,0)=u_t (x,0)=0

Provide complete and step by step solution for the question and show calculations and use formulas.