29 Tricomi PDE

 29.1 Boundary value problem for the Tricomi equation

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29.1 Boundary value problem for the Tricomi equation

problem number 166

From Mathematica DSolve helps pages.

Solve for \(u(x,y)\) \[ \frac{\partial ^2 u}{\partial x^2} + y \frac{\partial ^2 u}{\partial y^2} =0 \]

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

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