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I need to find a closed-form solution for the following PDE (a diffusion equation) on $u(x,t)$:

$$\frac{\partial u}{\partial t} = a\varepsilon^2 (x^2 u_x)_x$$

With $\varepsilon$ (an asymptotic parameter) and $a$ being real constants.

Please help. Thanks in advance.

Diptangshu
  • 93
  • When Maple is used, it always uses the separation of variables. For example, here too the same path has been taken. The issue is, is it necessary that the temporal part will always behave exponentially? – Diptangshu Oct 11 '20 at 10:21

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