1. The problem statement, all variables and given/known data The question is Ytt- c^2Yxx =0 on the doman 0<x< +infinity where initia conditions are y(x,0) = e^-x^2 = f(x) , Yt(x,0) =x*e^-x^2 = g(n) and boundary condition is y(0,t) = 0 and c = 2 2. Relevant equations D'Almbert solution 1/2(f(x+ct)+f(x-ct))+1/2c∫ g(n) dn over the limits (x+ct) to (x-ct) 3. The attempt at a solution So I just plugged in the f(x) and g(x) in the D'alembert solution to get 1/2(e^-(x+2t)^2+e^-(x-2t)^2)+1/4 ∫ g(n) but since we need to make it an odd function to apply D'alembert I then did -f(x) = f(-x) and -g(x) = g(-x) So I split the ∫ g(n) into two parts which are ∫g(n) over the limits 0 to x-2t + ∫g(n) over the limits x+2t to 0 then in order to give it oddness to the first part I did -∫g(-n) over the limits 0 to x-2t so the limits changed to 0 to x+2t and finally I ended up with 1/4( ∫-1/2*e^-x^2 over the limits 0 to x+2t + ∫-1/2*e^-x^2 over the limits x+2t to 0) integration of x*e^-x^2 = -1/2*e^-x^2. As for the f(x) we know f(-x) = -f(x) so I did 1/2(1/2(e^-(x+2t)^2-e^-(x+2t)^2) to give it oddness, now that both functions have been given oddness my wave solution is 1/2(1/2(e^-(x+2t)^2-e^-(x+2t)^2)+ 1/4( ∫-1/2*e^-x^2 over the limits 0 to x+2t + ∫-1/2*e^-x^2 over the limits x+2t to 0) When I apply the boundary condition y(0,t) = 0 I see that the f(x) term 1/2(1/2(e^-(x+2t)^2-e^-(x+2t)^2) = 0. As for the g(n) part after applying the limits and boundary condition I end up with 1/4(-1/2+1/2*e^-(2t)^2+ -1/2 *e^-(2t)^2 + 1/2) = 0 Can you please tell me if everything I did above was the correct way to do it. Many thanks.