\[ y'(x)=2 x-F(x) \left (-x^4+2 x^2 y(x)-y(x)^2+1\right ) \] ✓ Mathematica : cpu = 0.196767 (sec), leaf count = 58
\[\left \{\left \{y(x)\to \frac {\exp \left (\int _1^x2 F(K[5])dK[5]\right )}{-\int _1^x\exp \left (\int _1^{K[6]}2 F(K[5])dK[5]\right ) F(K[6])dK[6]+c_1}+x^2+1\right \}\right \}\] ✓ Maple : cpu = 0.465 (sec), leaf count = 44
\[y \relax (x ) = \frac {-x^{2} {\mathrm e}^{\int 2 F \relax (x )d x}+c_{1} x^{2}+{\mathrm e}^{\int 2 F \relax (x )d x}+c_{1}}{-{\mathrm e}^{\int 2 F \relax (x )d x}+c_{1}}\]