I would really appreciate an hint on how to get the exact solution of this linear ODE
\begin{equation} y'' + e^{x^2}y=0, \end{equation}
with initial conditions given by $y(0)=1$ and $y'(0)=0$.
I already know, from qualitative study and numerical simulations, how the solution behave, but I have no idea on how to get it in closed form.