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

problem number 102

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


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

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