\[ y'(x)=\frac {y(x)}{x}-F(x) \left (-x^3-7 x y(x)^2\right ) \] ✓ Mathematica : cpu = 0.108445 (sec), leaf count = 36
\[\left \{\left \{y(x)\to \frac {x \tan \left (\sqrt {7} \left (\int _1^x K[1]^2 F(K[1]) \, dK[1]+c_1\right )\right )}{\sqrt {7}}\right \}\right \}\]
✓ Maple : cpu = 0.038 (sec), leaf count = 25
\[ \left \{ y \left ( x \right ) ={\frac {\tan \left ( \left ( \int \!F \left ( x \right ) {x}^{2}\,{\rm d}x+{\it \_C1} \right ) \sqrt {7} \right ) x\sqrt {7}}{7}} \right \} \]