\[
\boxed{
{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left( x \right) + \left( 1/2\,{\frac {{\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}g \left( x \right) }{{\frac {\rm d}{{\rm d}x}}g \left( x \right) }}-3/4\,{\frac { \left( {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}g \left( x \right)  \right) ^{2}}{ \left( {\frac {\rm d}{{\rm d}x}}g \left( x \right)  \right) ^{2}}}+{\frac { \left( 1/4-{v}^{2} \right)  \left( {\frac {\rm d}{{\rm d}x}}g \left( x \right)  \right) ^{2}}{g \left( x \right) }}+ \left( {\frac {\rm d}{{\rm d}x}}g \left( x \right)  \right) ^{2} \right) y \left( x \right) =0}
\]