Exponential function

In the equation environment, you shouldn't use the $ sign(*):

\begin{equation} e^{y^2/4} \end{equation}

or

\begin{equation} e^{\frac{1}{4} y^2} \end{equation}

should work.

(*) Except in such cases:

\begin{equation} x=0 \text{ if $x$ and $y$ are nice people} \end{equation}