Solve U_xx=U_tt with c=1. Dirchlet boundary conditions U(x,0)=1 for 5<x<7 U(x,0)=0 for everywhere else U_t(x,0)=0 I know that by taken an odd extension I can get rid of the boundary condition and then solve the initial value problem using the d'alembert solution and only care for x>0 Graphically I know it will be square wave that break off in opposite directions and has amplitude of 1/2. At the origin the square wave will die while on the other side it will go on forever. What is tripping me up are the constant initial conditions. When I plug them in I get for x>t U(x,t)=1 and for t>x I get 0. This doesn't sound right to me. Any help will be appreciated.