I was trying solve infinite rope,I need to solve this problem with a different method than the traditional one, (homogeneous case, with D'alambert). Using Fourier transform I think it could be easier but I have not been able to achieve it, can you help me?
$$u_{tt}-c^2u_{xx}=0, -\infty<x<\infty, t>0 $$ $u(x,0)=f(x), u_{t}(x,0)=g(x), \infty<x<\infty$