2.1.33 \(x u_x+y u_y=x e^{-u}\) with \(u=0\) on \(y=x^2\) Example 3.5.10 in Lokenath Debnath

problem number 33

Added June 2, 2019.

From example 3.5.10, page 218 nonlinear pde’s by Lokenath Debnath, 3rd edition.

Solve for \(u(x,y)\) \begin {align*} x u_x+y u_y &=x e^{-u} \end {align*}

with \(u=0\) on \(y=x^2\)

Mathematica


\[\left \{\left \{u(x,y)\to \log \left (-\frac {y}{x}+x+1\right )\right \}\right \}\]

Maple


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

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