2.1.49 \(y u_x+x u_y=x y\) with \(u(0,y)=e^{-y^2},u(x,0)=e^{-x^2}\). Problem 3.5(e) Lokenath Debnath

problem number 49

Added June 3, 2019.

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

Solve for \(u(x,y)\) \[ y u_x+x u_y=x y \] with \(u(0,y)=e^{-y^2},u(x,0)=e^{-x^2}\) for \(x>0,y>0\)

Mathematica ✗

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

Failed

Maple ✗

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

sol=()

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