# Method of simplifying parabolic PDE

I consider PDE for the function $$f(x, t)$$ of the form:

\begin{aligned} f_t + Ax^2 f_{xx} + Bx f_{x} + g(x)f + h(x, t) = 0 \\ f(x, T) = 0 \end{aligned}

where $$f:\mathbb{R}^{+}\times [0, T] \rightarrow \mathbb{R}$$.

This is very general form of PDE, but I wonder what kind of substitution or other method I can use to simplify it and finally solve.

• The $x$ part looks like a Cauchy-Euler form, so maybe try $x = e^y$? – Dylan Mar 6 at 11:04