2.1.32 \(y u_x+x u_y=u\) with \(u(x,0)=x^3\) and \(u(0,y)=y^3\) Example 3.5.8 in Lokenath Debnath

problem number 32

Added June 2, 2019.

From example 3.5.8, page 216 nonlinear pde’s by Lokenath Debnath, 3rd edition.

Solve for \(u(x,y)\) \begin {align*} y u_x+x u_y&=u \end {align*}

with with \(u(x,0)=x^3\) and \(u(0,y)=y^3\)

Mathematica ✗

ClearAll["Global`*"]; 
pde =  y*D[u[x, y], x] +x*D[u[x, y], y] ==u[x,y]; 
ic  = {u[x,0]==x^3,u[0,y]==y^3}; 
sol =  AbsoluteTiming[TimeConstrained[DSolve[{pde,ic} ,u[x, y], {x, y}], 60*10]];
 

Failed

Maple ✗

restart; 
pde :=y*diff(u(x,y),x)+x*diff(u(x,y),y)=u(x,y); 
ic  := u(x,0)=x^3,u(0,y)=y^3; 
cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve([pde,ic],u(x,y))),output='realtime'));
 

sol=()

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