\[ y'(x)=-\frac {1}{2} x \left (a x^2-2 F\left (\frac {a x^4}{8}+y(x)\right )\right ) \] ✓ Mathematica : cpu = 0.217244 (sec), leaf count = 126
\[\text {Solve}\left [\int _1^{y(x)}-\frac {F\left (\frac {a x^4}{8}+K[2]\right ) \int _1^x\frac {a K[1]^3 F'\left (\frac {1}{8} a K[1]^4+K[2]\right )}{2 F\left (\frac {1}{8} a K[1]^4+K[2]\right )^2}dK[1]+1}{F\left (\frac {a x^4}{8}+K[2]\right )}dK[2]+\int _1^x\left (K[1]-\frac {a K[1]^3}{2 F\left (\frac {1}{8} a K[1]^4+y(x)\right )}\right )dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.209 (sec), leaf count = 31
\[ \left \{ y \left ( x \right ) =-{\frac {a{x}^{4}}{8}}+{\it RootOf} \left ( -{x}^{2}+2\,\int ^{{\it \_Z}}\! \left ( F \left ( {\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}+2\,{\it \_C1} \right ) \right \} \]