\[ y'(x)=\frac {(a-1) (a+1) x}{a^2 F\left (-\frac {1}{2} a^2 x^2+\frac {x^2}{2}+\frac {y(x)^2}{2}\right )-F\left (-\frac {1}{2} a^2 x^2+\frac {x^2}{2}+\frac {y(x)^2}{2}\right )+y(x)} \] ✓ Mathematica : cpu = 0.389328 (sec), leaf count = 177
\[\text {Solve}\left [\int _1^{y(x)}\left (\frac {K[2]}{(a-1) (a+1) F\left (-\frac {1}{2} a^2 x^2+\frac {x^2}{2}+\frac {K[2]^2}{2}\right )}-\int _1^x\frac {K[1] K[2] F'\left (-\frac {1}{2} a^2 K[1]^2+\frac {K[1]^2}{2}+\frac {K[2]^2}{2}\right )}{F\left (-\frac {1}{2} a^2 K[1]^2+\frac {K[1]^2}{2}+\frac {K[2]^2}{2}\right )^2}dK[1]+1\right )dK[2]+\int _1^x-\frac {K[1]}{F\left (-\frac {1}{2} a^2 K[1]^2+\frac {K[1]^2}{2}+\frac {y(x)^2}{2}\right )}dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.461 (sec), leaf count = 60
\[\frac {y \relax (x )}{\left (a -1\right ) \left (a +1\right )}+\frac {\int _{}^{-a^{2} x^{2}+x^{2}+y \relax (x )^{2}}\frac {1}{F \left (\frac {\textit {\_a}}{2}\right )}d \textit {\_a}}{2 a^{4}-4 a^{2}+2}-c_{1} = 0\]