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