2.16.5 \(u_{xy} = \sin (x) \sin (y) \)

problem number 144

Added December 20, 2018.

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

PDE solved by Laplace transform. Solve for \(u(x,y)\) \[ u_{xy} = \sin (x) \sin (y) \] With boundary conditions \begin {align*} u(x,0)&=1+\cos (x) \\ \frac {\partial u}{\partial y}(0,y) &= -2 \sin y \end {align*}

Mathematica


\[\{\{u(x,y)\to (\cos (x)+1) \cos (y)\}\}\]

Maple


\[u \left (x , y\right ) = \left (\cos (x )+1\right ) \cos (y )\]

________________________________________________________________________________________