I was solving an example of 1D wave equation with given BC and IC by separation of variables and Fourier series. $$\frac{\partial^2u}{\partial t^2}=c^2\frac{\partial^2u}{\partial x^2} $$ $$BC: u(0,t)=u(l,t)=0$$ $$IC:u(x,0)=\sin\left(\frac{\pi}{l} x\right) $$$$\partial_tu(x,0)=0$$ By separating th...