\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =-F \left ( x \right ) \left ( -7\,x \left ( y \left ( x \right ) \right ) ^{2}-{x}^{3} \right ) +{\frac {y \left ( x \right ) }{x}}=0} \]
Mathematica: cpu = 0.106513 (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 = 0.031 (sec), leaf count = 25 \[ \left \{ y \left ( x \right ) ={\frac {\tan \left ( \left ( \int \!F \left ( x \right ) {x}^{2}\,{\rm d}x+{\it \_C1} \right ) \sqrt {7} \right ) x\sqrt {7}}{7}} \right \} \]