Added Jan 10, 2019.
Solve for
Mathematica ✓
ClearAll["Global`*"]; lap = Laplacian[u[r, theta, phi, t], {r, theta, phi}, "Spherical"]; pde = D[u[r, theta, phi, t], {t, 2}] == c^2*lap; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[r, theta, phi, t], {r, theta, phi, t}, Assumptions -> {0 < theta < Pi}], 60*10]];
Maple ✓
restart; lap:=VectorCalculus:-Laplacian( u(r,theta,phi,t), 'spherical'[r,theta,phi] ); pde := diff(u(r,theta,phi,t),t$2)= c^2* lap; cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,u(r,theta,phi,t),'build') assuming 0<theta,theta<Pi),output='realtime')); sol := simplify(sol);
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