\[ y'(x)=-\frac {1}{2} x \left (a x^2-2 F\left (\frac {a x^4}{8}+y(x)\right )\right ) \] ✓ Mathematica : cpu = 51.4666 (sec), leaf count = 111
\[\text {Solve}\left [c_1=\int _1^{y(x)} \left (-\int _1^x \frac {a K[1]^3 F'\left (\frac {1}{8} a K[1]^4+K[2]\right )}{2 F\left (\frac {1}{8} a K[1]^4+K[2]\right )^2} \, dK[1]-\frac {1}{F\left (K[2]+\frac {a x^4}{8}\right )}\right ) \, dK[2]+\int _1^x \left (K[1]-\frac {a K[1]^3}{2 F\left (\frac {1}{8} a K[1]^4+y(x)\right )}\right ) \, dK[1],y(x)\right ]\]
✓ Maple : cpu = 0.152 (sec), leaf count = 31
\[ \left \{ y \left ( x \right ) =-{\frac {a{x}^{4}}{8}}+{\it RootOf} \left ( -{x}^{2}+2\,\int ^{{\it \_Z}}\! \left ( F \left ( {\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}+2\,{\it \_C1} \right ) \right \} \]