Use separation of variables to solve the wave equation:


on the domain $0<x<1$,$t>0$, with initial conditions


$$u_t(x,0)=\cos(\pi x)$$

and boundary conditions


So I have rewrote this as


then I set


Then I got loss.

  • $\begingroup$ Welcome to MSE. :) As this site is not solving home-works, you should show what you think and what you have tried to solve this problem. If you don't after a while your question will be closed. :) $\endgroup$ – H. R. Nov 23 '15 at 11:53
  • $\begingroup$ This is what I've done. @Normal Human $\endgroup$ – Jack Nov 23 '15 at 13:36

Hint: Just solve the equation using the standard separate of variable approach with initial condition as a sinusoidal function. Be sure you can generalize this approach to dealing with any other initial conditions using Fourier series.


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