2.1.67 \((y+u)u_x+(x+u)u_y=x+y\). Problem 3.17(a) Lokenath Debnath

problem number 67

Added June 3, 2019.

Problem 3.17(a) nonlinear pde’s by Lokenath Debnath, 3rd edition.

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

Mathematica


$Aborted

Maple


\[u \left (x , y\right ) = \frac {-\RootOf \left (\left (c_{1} {\mathrm e}^{\frac {3 c_{1} c_{2}}{y}}+{\mathrm e}^{\frac {3 c_{1} c_{2}}{y}}\right ) \mathit {\_Z}^{9}-c_{1}^{3} x^{3}-3 c_{1}^{2} x^{2} y -3 c_{1} x y^{2}+\left (3 c_{1}^{3} x^{3}+9 c_{1}^{2} x^{2} y +9 c_{1} x y^{2}+3 y^{3}\right ) \mathit {\_Z}^{3}-y^{3}\right )^{6} {\mathrm e}^{\frac {3 c_{1} c_{2}}{y}}-\left (x +y \right ) \left (c_{1} x +y \right )^{2}}{\left (c_{1} x +y \right )^{2}}\]

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