2.1.65 \(x u_x+y u_y=x y\) with \(u=\frac {x^2}{2}\) at \(y=x\). Problem 3.14(g) Lokenath Debnath

problem number 65

Added June 3, 2019.

Problem 3.14(g) nonlinear pde’s by Lokenath Debnath, 3rd edition.

Solve for \(u(x,y)\) \[ x u_x+y u_y=x y \] With \(u=\frac {x^2}{2}\) at \(y=x\).

Mathematica


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

Maple


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

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