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