2.8.1 \(u_{xx} + y u_{yy} = 0\) with \(u(x,0)=0,u_y(x,0)=x^2\)

problem number 99

From Mathematica DSolve helps pages.

Boundary value problem for the Tricomi equation.

Solve for \(u(x,y)\) \[ u_{xx} + y u_{yy} = 0 \] With boundary conditions \begin {align*} u(x,0)&=0 \\ \frac {\partial u}{\partial y}(x,0) &= x^2 \end {align*}

Mathematica


\[\left \{\left \{u(x,y)\to -y \left (y-x^2\right )\right \}\right \}\]

Maple


\[u \left (x , y\right ) = \left (x^{2}-y \right ) y\]

________________________________________________________________________________________