I want to solve a PDE realated to heat equation with exponential additive term
$${\partial u\over\partial t}={1\over x^2}{\partial\over\partial x}(x^2{\partial u\over\partial x})+e^u$$
I dervived this equation from thermal explosion's equation so it is similar to heat equation with reaction term $e^u$
Does this equation has analytic solution? If so, what is it?