\[ y'(x)=\frac {y(x)}{x}-F(x) \left (-x^3-7 x y(x)^2\right ) \] ✓ Mathematica : cpu = 0.120685 (sec), leaf count = 43
\[\left \{\left \{y(x)\to \frac {x \tan \left (\sqrt {7} \int _1^xF(K[1]) K[1]^2dK[1]+\sqrt {7} c_1\right )}{\sqrt {7}}\right \}\right \}\] ✓ Maple : cpu = 0.22 (sec), leaf count = 25
\[ \left \{ y \left ( x \right ) ={\frac {\tan \left ( \left ( \int \!{x}^{2}F \left ( x \right ) \,{\rm d}x+{\it \_C1} \right ) \sqrt {7} \right ) x\sqrt {7}}{7}} \right \} \]