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