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

problem number 100

Added June 20, 2019

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

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

Mathematica


Failed

Maple


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