\[
\boxed{
 \left( {\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left( x \right)  \right)  \left( \sin \left( x \right)  \right) ^{2}+3\, \left( {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left( x \right)  \right) \sin \left( x \right) \cos \left( x \right) + \left( \cos \left( 2\,x \right) +4\,\nu\, \left( \nu+1 \right)  \left( \sin \left( x \right)  \right) ^{2} \right) {\frac {\rm d}{{\rm d}x}}y \left( x \right) +2\,\nu\, \left( \nu+1 \right) y \left( x \right) \sin \left( 2\,x \right) =0}
\]