\[
\boxed{
{x}^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left( x \right) +3\,x{\frac {\rm d}{{\rm d}x}}y \left( x \right) + \left( -{v}^{2}+{x}^{2}+1 \right) y \left( x \right) -f \left( x \right) =0}
\]