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For example:

$\frac{\partial^2 u}{\partial x^2}+4\frac{\partial^2 u}{\partial x \partial y} + 3\frac{\partial^2 u}{\partial y^2}=0$

Replacement:

$\left\{\begin{matrix}\xi & = & y & - & 3x\\ \eta & = & y & - & x\end{matrix}\right.$

Now we have to calculate partial derivatives:

$\frac{\partial^2 u}{\partial x^2}=\frac{\partial }{\partial x}\left (\frac{\partial u}{\partial \xi} \frac{\partial \xi}{\partial x}+\frac{\partial u}{\partial \eta}\frac{\partial \eta}{\partial x} \right )=...$

Question: Is there a convenient way in Mathematica?

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