I have this equation to solve \begin{equation} \partial_t F = \partial^2_y F \end{equation} and got two independent solutions through some trial and error.
\begin{equation} F_1 = erf\left(\frac{y}{2\sqrt{t}}\right) \\ F_2 = \frac{1}{\sqrt{t}}\exp\left( \frac{-y^2}{4{t}}\right) \end{equation} I'm wondering how many other possible solutions exist to this equation. I'll be glad to be directed to a chapter in some mathematics text that deals with the number of solutions for a linear partial differential equation.
