Added June 20, 2019
Taken from http://people.maths.ox.ac.uk/chengq/outreach/The%20Tricomi%20Equation.pdf
Solve for \(u(x,y)\) \[ u_{xx} + x u_{yy} = 0 \]
Mathematica ✗
ClearAll["Global`*"]; pde = D[u[x, y], {x, 2}] + x*D[u[x, y], {y, 2}] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, y], {x, y}], 60*10]];
Failed
Maple ✓
restart; pde := diff(u(x,y),x$2)+ x*diff(u(x,y),y$2)=0; cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,u(x,y),'build')),output='realtime'));
\[u \left (x , y\right ) = \left (c_{1} \AiryAi \left (-\left (-\mathit {\_c}_{1}\right )^{\frac {1}{3}} x \right )+c_{2} \AiryBi \left (-\left (-\mathit {\_c}_{1}\right )^{\frac {1}{3}} x \right )\right ) \left (c_{3} \sin \left (y \sqrt {\mathit {\_c}_{1}}\right )+c_{4} \cos \left (y \sqrt {\mathit {\_c}_{1}}\right )\right )\]