2.1.60 \((u_x+u_y)^2-u^2=0\). Problem 3.10 Lokenath Debnath

problem number 60

Added June 3, 2019.

Problem 3.10 nonlinear pde’s by Lokenath Debnath, 3rd edition.

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

Mathematica


\begin {align*} & \left \{u(x,y)\to e^{-x} c_1(y-x)\right \}\\& \left \{u(x,y)\to e^x c_1(y-x)\right \}\\ \end {align*}

Maple


\[u \left (x , y\right ) = c_{1} {\mathrm e}^{\frac {y \mathit {\_c}_{2}+x}{\mathit {\_c}_{2}+1}}\]

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