Added June 20, 2019
Taken from http://people.maths.ox.ac.uk/chengq/outreach/The%20Tricomi%20Equation.pdf
Solve for \(u(x,y)\) \[ x u_{xx} + u_{yy} = 0 \]
Mathematica ✗
ClearAll["Global`*"]; pde = x*D[u[x, y], {x, 2}] + D[u[x, y], {y, 2}] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, y], {x, y}], 60*10]];
Failed
Maple ✓
restart; pde := x*diff(u(x,y),x$2)+ diff(u(x,y),y$2)=0; cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,u(x,y),'build')),output='realtime'));
\[u \left ( x,y \right ) =\sqrt {x} \left ( \BesselJ \left ( 1,2\,\sqrt {-{\it \_c}_{{1}}}\sqrt {x} \right ) {\it \_C1}+\BesselY \left ( 1,2\,\sqrt {-{\it \_c}_{{1}}}\sqrt {x} \right ) {\it \_C2} \right ) \left ( {\it \_C3}\,\sin \left ( \sqrt {{\it \_c}_{{1}}}y \right ) +{\it \_C4}\,\cos \left ( \sqrt {{\it \_c}_{{1}}}y \right ) \right ) \]