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


\[u \left (x , y\right ) = \left (c_{1} \BesselJ \left (1, 2 \sqrt {-\mathit {\_c}_{1}}\, \sqrt {x}\right )+c_{2} \BesselY \left (1, 2 \sqrt {-\mathit {\_c}_{1}}\, \sqrt {x}\right )\right ) \left (c_{3} \sin \left (y \sqrt {\mathit {\_c}_{1}}\right )+c_{4} \cos \left (y \sqrt {\mathit {\_c}_{1}}\right )\right ) \sqrt {x}\]