2.1.69 \((x+y) u_x + (x-y)u_y =0\). Problem 3.17(c) Lokenath Debnath

problem number 69

Added June 3, 2019.

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

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

Mathematica


\begin {align*} & \left \{u(x,y)\to c_1\left (\log \left (-\sqrt {-x^2+2 x y+y^2}\right )\right )\right \}\\& \left \{u(x,y)\to c_1\left (\frac {1}{2} \log \left (-x^2+2 x y+y^2\right )\right )\right \}\\ \end {align*}

Maple


\[u \left (x , y\right ) = \mathit {\_F1} \left (-\frac {1}{\sqrt {-x^{2}+2 x y +y^{2}}}\right )\]

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