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