\[ y'(x)=\frac {y(x)}{x}-F(x) \left (x^2+2 x y(x)-y(x)^2\right ) \] ✓ Mathematica : cpu = 0.175165 (sec), leaf count = 104
\[\left \{\left \{y(x)\to -\frac {x \left (-\exp \left (2 \sqrt {2} \left (\int _1^xF(K[1]) K[1]dK[1]+c_1\right )\right )+\sqrt {2} \exp \left (2 \sqrt {2} \left (\int _1^xF(K[1]) K[1]dK[1]+c_1\right )\right )-1-\sqrt {2}\right )}{1+\exp \left (2 \sqrt {2} \left (\int _1^xF(K[1]) K[1]dK[1]+c_1\right )\right )}\right \}\right \}\] ✓ Maple : cpu = 0.178 (sec), leaf count = 29
\[ \left \{ y \left ( x \right ) ={\frac {x \left ( \sqrt {2}-2\,\tanh \left ( \left ( {\it \_C1}+\int \!F \left ( x \right ) x\,{\rm d}x \right ) \sqrt {2} \right ) \right ) \sqrt {2}}{2}} \right \} \]