2.16.3 \( u_{xx} + y u_{yy} = 0\)

problem number 142

Added December 20, 2018.

Taken from https://www.mapleprimes.com/posts/209970-Exact-Solutions-For-PDE-And-Boundary--Initial-Conditions-2018

Laplace like PDE with polynomial solution. Solve for \(u(x,y)\) \[ u_{xx} + y u_{yy} = 0 \] With boundary conditions \begin {align*} u(x,0)&=0 \\ \frac {\partial u}{\partial y}(x,0) &=x^2 \end {align*}

Mathematica


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

Maple


\[u \left (x , y\right ) = \left (x^{2}-y \right ) y\]

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