\[ y'(x)=-\frac {1}{2} x \left (a x^2-2 F\left (\frac {a x^4}{8}+y(x)\right )\right ) \] ✓ Mathematica : cpu = 0.278387 (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 = 0.148 (sec), leaf count = 31
\[\left \{y \left (x \right ) = -\frac {a \,x^{4}}{8}+\RootOf \left (-x^{2}+2 c_{1}+2 \left (\int _{}^{\textit {\_Z}}\frac {1}{F \left (\textit {\_a} \right )}d \textit {\_a} \right )\right )\right \}\]