#### 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

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

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