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