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