2.1.38 \((1+x^2) u_x+ u_y=0\) Problem 3.3(d) Lokenath Debnath

problem number 38

Added June 2, 2019.

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

Solve for \(u(x,y)\)

\[ (1+x^2) u_x+ u_y=0 \]

Mathematica ✓

ClearAll["Global`*"]; 
pde =  (1+x^2)*D[u[x, y], x] + D[u[x, y], y] ==0; 
sol =  AbsoluteTiming[TimeConstrained[DSolve[pde ,u[x, y], {x, y}], 60*10]];
 

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

Maple ✓

restart; 
pde :=(1+x^2)*diff(u(x,y),x)+diff(u(x,y),y)=0; 
cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,u(x,y))),output='realtime'));
 

\[u \left (x , y\right ) = f_{1} \left (-\arctan \left (x \right )+y \right )\]

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