2.1.47 $x{u}_x+y{u}_y=2xy$ with $u=2$ on $y=x^2$. Problem 3.5(c) Lokenath Debnath

problem number 47

Added June 3, 2019.

Problem 3.5(c) nonlinear pde’s by Lokenath Debnath, 3rd edition.

Solve for $u(x,y)$ $$x{u}_x+y{u}_y=2xy$$ with with $u=2$ on $y=x^2$.

Mathematica ✓

ClearAll["Global`*"]; 
pde =  x*D[u[x, y], x] + y*D[u[x,y],y] == 0; 
ic  = u[x,x^2]==2; 
sol =  AbsoluteTiming[TimeConstrained[DSolve[{pde,ic} ,u[x, y], {x, y}], 60*10]];
 

$$\{\{u(x,y)\to 2\}\}$$

Maple ✓

restart; 
pde :=x*diff(u(x,y),x)+ y*diff(u(x,y),y)= 0; 
ic  := u(x,x^2)=2; 
cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,u(x,y))),output='realtime'));
 

$$u(x,y)=\mathit{\_}\mathit{F}\mathit{1}\left(\frac{y}{x}\right)$$ Maple does not accept this form of Cauchy data as I.C.

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