2.9.1 \(x u_{xx} + u_{yy} = 0\)

problem number 101

Added June 20, 2019

Taken from http://people.maths.ox.ac.uk/chengq/outreach/The%20Tricomi%20Equation.pdf

Solve for \(u(x,y)\) \[ x u_{xx} + u_{yy} = 0 \]

Mathematica


Failed

Maple


\[u \left ( x,y \right ) =\sqrt{x} \left ( \BesselJ \left ( 1,2\,\sqrt{-{\it \_c}_{{1}}}\sqrt{x} \right ){\it \_C1}+\BesselY \left ( 1,2\,\sqrt{-{\it \_c}_{{1}}}\sqrt{x} \right ){\it \_C2} \right ) \left ({\it \_C3}\,\sin \left ( \sqrt{{\it \_c}_{{1}}}y \right ) +{\it \_C4}\,\cos \left ( \sqrt{{\it \_c}_{{1}}}y \right ) \right ) \]