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Added March 28, 2019.
Problem 1, section 41, Fourier series and boundary value problems 8th edition by Brown and Churchill.
Solve \(u_t = \nabla u \) where \(\nabla u = \frac {1}{r} (r u)_{rr} \) in Spherical coordinates with initial conditions \(u(r,0)=0\) and boundary conditions \(u(1,t)=t\)
Mathematica ✗
ClearAll[r, t, u, k]; pde = D[u[r, t], t] == (k*D[r*u[r, t], {r, 2}])/r; ic = u[r, 0] == 0; bc = u[1, t] == t; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic, bc}, u[r, t], {r, t}, Assumptions -> {t > 0, k > 0}], 60*10]];
\[ \text {Failed} \]
Maple ✓
r:='r'; u:='u'; t:='t';theta:='theta';k:='k'; pde:=diff(u(r,t),t)= k/r*diff(r*u(r,t),r$2); ic:=u(r,0)=0; bc := u(1,t) =t; cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve([pde,ic,bc],u(r,t),HINT =boundedseries(r=0)) assuming t>0,k>0) ,output='realtime'));
\[ u \left ( r,t \right ) ={\frac {1}{r} \left ( -{\it invlaplace} \left ( {{\it \_F2} \left ( s \right ) \sinh \left ( {\frac {\sqrt {s}r}{\sqrt {k}}} \right ) \cosh \left ( {\frac {\sqrt {s}}{\sqrt {k}}} \right ) \left ( \sinh \left ( {\frac {\sqrt {s}}{\sqrt {k}}} \right ) \right ) ^{-1}},s,t \right ) +{\it invlaplace} \left ( {\frac {1}{{s}^{2}}\sinh \left ( {\frac {\sqrt {s}r}{\sqrt {k}}} \right ) \left ( \sinh \left ( {\frac {\sqrt {s}}{\sqrt {k}}} \right ) \right ) ^{-1}},s,t \right ) +{\it invlaplace} \left ( {\it \_F2} \left ( s \right ) \cosh \left ( {\frac {\sqrt {s}r}{\sqrt {k}}} \right ) ,s,t \right ) \right ) } \] Has unresolved Laplace integrals