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I have a question regarding a PDE (Fokker-Planck) and change of variables. I have a problem deciding what route to take after I use the chain route. I have an expression $$\frac{\partial u}{\partial t} = \frac{\partial}{\partial x}\left(\frac{\partial}{\partial x}+x\right)u$$ and would like the variables substitution $$x = Xe^{-t} \text{ and } u=ve^t.$$ This give $$\frac{\partial v}{\partial t} = e^{2t} \frac{\partial^2 v}{\partial X^2}.$$ I thank you for your help.

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    What is the expanded form of $\dfrac{\partial}{\partial x}\left(\dfrac{\partial}{\partial x}+x\right)u$ ?2012-08-02
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    This question has been solved perfectly. Hope that the asker has been diving enough and accept the answer at an early date.2012-09-10

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