2.1.42 \(y u_y - x u_x = 1\) Problem 3.3(h) Lokenath Debnath

problem number 42

Added June 3, 2019.

Problem 3.3(h) nonlinear pde’s by Lokenath Debnath, 3rd edition.

Solve for \(u(x,y)\) \[ y u_y- x u_x=1 \]

Mathematica

ClearAll["Global`*"]; 
pde =  y*D[u[x, y], y] - x*D[u[x, y], x] ==1; 
sol =  AbsoluteTiming[TimeConstrained[DSolve[pde ,u[x, y], {x, y}], 60*10]];
 

\[\{\{u(x,y)\to -\log (x)+c_1(x y)\}\}\]

Maple

restart; 
pde :=y*diff(u(x,y),y)- x*diff(u(x,y),x)=1; 
cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,u(x,y))),output='realtime'));
 

\[u \left (x , y\right ) = \textit {\_F1} \left (x y \right )-\ln \left (x \right )\]

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