\[ y'(x)=2 x-F(x) \left (2 x^2 y(x)-x^4-y(x)^2+1\right ) \] ✓ Mathematica : cpu = 0.204567 (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 = 1.428 (sec), leaf count = 44
\[ \left \{ y \left ( x \right ) ={\frac {-{x}^{2} \left ( {{\rm e}^{\int \!F \left ( x \right ) \,{\rm d}x}} \right ) ^{2}+{\it \_C1}\,{x}^{2}+ \left ( {{\rm e}^{\int \!F \left ( x \right ) \,{\rm d}x}} \right ) ^{2}+{\it \_C1}}{- \left ( {{\rm e}^{\int \!F \left ( x \right ) \,{\rm d}x}} \right ) ^{2}+{\it \_C1}}} \right \} \]