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I have found the solution of the PDE:

$ y u_x +x^3 u_y = x^3 y \quad $ with boundary condition: $ \quad u(x,x^2) = x^4, \quad x \geq 2 $

to be $ \quad u(x,y) = \frac{3}{2} y^2 - \frac{1}{2}x^4 \quad $ and verified the solution. The next part is to specify the range for which the solution is valid. I know it should be fairly straightforward, but can't find any notes on it.

Any help appreciated.

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I'll rephrase the question: what conditions, if any, must be imposed on the numbers $x$ and $y$, so that (a) the function $u(x,y)$ is defined; (b) all the necessary derivatives of $u$ exist and satisfy the given equation? – user53153 Jan 2 '13 at 23:37

This is just a piece of cake. The solution is valid for $x,y\in\mathbb{C}$ .

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