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'));
\[u \left (x , y\right ) = \left (c_{1} \BesselJ \left (1, 2 \sqrt {-\mathit {\_c}_{1}}\, \sqrt {x}\right )+c_{2} \BesselY \left (1, 2 \sqrt {-\mathit {\_c}_{1}}\, \sqrt {x}\right )\right ) \left (c_{3} \sin \left (y \sqrt {\mathit {\_c}_{1}}\right )+c_{4} \cos \left (y \sqrt {\mathit {\_c}_{1}}\right )\right ) \sqrt {x}\]