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