\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =-F \left ( x \right ) \left ( -a{x}^{2}+ \left ( y \left ( x \right ) \right ) ^{2} \right ) +{\frac {y \left ( x \right ) }{x}}=0} \]
Mathematica: cpu = 0.099513 (sec), leaf count = 40 \[ \left \{\left \{y(x)\to \sqrt {a} x \tanh \left (\sqrt {a} \int _1^x K[1] F(K[1]) \, dK[1]+\sqrt {a} c_1\right )\right \}\right \} \]
Maple: cpu = 0.047 (sec), leaf count = 26 \[ \left \{ y \left ( x \right ) =\tanh \left ( \int \!F \left ( x \right ) x \,{\rm d}x\sqrt {a}+{\it \_C1}\,\sqrt {a} \right ) x\sqrt {a} \right \} \]