2.1.43 \(u_x+2 x y^2 u_y=0\) Problem 3.4 Lokenath Debnath

problem number 43

Added June 3, 2019.

Problem 3.4 nonlinear pde’s by Lokenath Debnath, 3rd edition.

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

\[ u_x+2 x y^2 u_y=0 \]

Mathematica ✓

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

\[\left \{\left \{u(x,y)\to c_1\left (-\frac {x^2 y+1}{y}\right )\right \}\right \}\]

Maple ✓

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

\[u \left (x , y\right ) = f_{1} \left (\frac {y \,x^{2}+1}{y}\right )\]

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