Heaviside function and neumann boundary condition

Question

Problems:

Green's Functions, Wave Equation, Heaviside Function and Neumann Boundary Condition

The Green's function for the infinite domain is

                   G(x,t) = 1/2c (H(x + ct) - H(x-ct))

where H is the Heaviside function. Use Green's functions to solve the Neumann boundary condition problem...

                                 u_tt = u_xx + ƒ (x,t) 00

                                 u(x,0) = 0 u_t(x,0) = 0 u_x (0,t) = 0

Give explicit formulas for the solution in each region x>t and x