2.10.1 \(u_{xx} + u_{yy} + \frac{\beta }{x} u_x = 0\)

problem number 103

Added June 20, 2019

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

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

Mathematica

Failed

Maple

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

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