\[ y'(x)=\frac {y(x)}{x}-F(x) \left (-x^3-7 x y(x)^2\right ) \] ✓ Mathematica : cpu = 0.141589 (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 = 0.042 (sec), leaf count = 25
\[\left \{y \left (x \right ) = \frac {\sqrt {7}\, x \tan \left (\left (c_{1}+\int x^{2} F \left (x \right )d x \right ) \sqrt {7}\right )}{7}\right \}\]