Added June 3, 2019.
Problem 3.5(d) nonlinear pde’s by Lokenath Debnath, 3rd edition.
Solve for \(u(x,y)\) \[ u_x+x u_y=0 \] with \(u(0,y)=\sin y\).
Mathematica ✓
ClearAll["Global`*"]; pde = D[u[x, y], x] + x*D[u[x,y],y] == 0; ic = u[0,y]==Sin[y]; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde,ic} ,u[x, y], {x, y}], 60*10]];
\[\left \{\left \{u(x,y)\to \sin \left (\frac {1}{2} \left (2 y-x^2\right )\right )\right \}\right \}\]
Maple ✓
restart; pde := diff(u(x,y),x)+ x*diff(u(x,y),y)= 0; ic := u(0,y)=sin(y); cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve([pde,ic],u(x,y))),output='realtime'));
\[u \left ( x,y \right ) =-\sin \left ( {\frac {{x}^{2}}{2}}-y \right ) \]
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