2.1.39 \(2 x y u_x+(x^2+y^2)u_y=0\) Problem 3.3(e) Lokenath Debnath

problem number 39

Added June 2, 2019.

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

Solve for \(u(x,y)\) \[ 2 x y u_x+(x^2+y^2)u_y=0 \]

Mathematica


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

Maple


\[u \left (x , y\right ) = \mathit {\_F1} \left (\frac {-x^{2}+y^{2}}{x}\right )\]

________________________________________________________________________________________