\[ y'(x)=\frac {y(x)}{x}-F(x) \left (-x^3-7 x y(x)^2\right ) \] ✓ Mathematica : cpu = 0.107583 (sec), leaf count = 42
\[\left \{\left \{y(x)\to \frac {x \tan \left (\sqrt {7} \int _1^x K[1]^2 F(K[1]) \, dK[1]+\sqrt {7} c_1\right )}{\sqrt {7}}\right \}\right \}\]
✓ Maple : cpu = 0.035 (sec), leaf count = 25
\[ \left \{ y \left ( x \right ) ={\frac {\tan \left ( \left ( \int \!{x}^{2}F \left ( x \right ) \,{\rm d}x+{\it \_C1} \right ) \sqrt {7} \right ) x\sqrt {7}}{7}} \right \} \]