2.1.51 \(u u_x - u u_y= u^2 + (x+y)^2\) with \(u(x,0)=1\) Problem 3.5(h) Lokenath Debnath

problem number 51

Added June 3, 2019.

Problem 3.5(h) nonlinear pde’s by Lokenath Debnath, 3rd edition.

Solve for \(u(x,y)\) \[ u u_x-u u_y=u^2 + (x+y)^2 \] With \(u(x,0)=1\).

Mathematica


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

Maple


\[u \left (x , y\right ) = \sqrt {\left (\left (x +y \right )^{2}+1\right ) {\mathrm e}^{2 x} {\mathrm e}^{-2 x -2 y}-\left (x +y \right )^{2}}\]

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