I'm looking to Plot the PDE for a range of 't''s on u(x) plots. I have two boundary conditions. My solution is as follows:
WaveEquation = D[u[x, t], {x, 2}] - D[u[x, t], {t, 2}] == 0;
Bound1 = (D[u[x, t], t] /. t -> 0) == 0.5 ;
Bound2 = u[x, 0] == x*(1 - x);
sol = DSolve[{WaveEquation, Bound1, Bound2}, u[x, t], {x, t}]
which strangely outputs my input. I tried Plotting the solution on a 3D plot with:
Plot3D[u[x, t] /. sol, {x, 0, 1}, {t, 0, 5}]
and Mathematica returned a host of errors. Where am I going wrong?
