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?
