\[ y'(x)=\frac {y(x)}{x}-F(x) \left (-x^2-2 x y(x)+y(x)^2\right ) \] ✓ Mathematica : cpu = 0.203353 (sec), leaf count = 107
DSolve[Derivative[1][y][x] == y[x]/x - F[x]*(-x^2 - 2*x*y[x] + y[x]^2),y[x],x]
\[\left \{\left \{y(x)\to -\frac {x \left (-\exp \left (2 \sqrt {2} \left (\int _1^x-F(K[1]) K[1]dK[1]+c_1\right )\right )+\sqrt {2} \exp \left (2 \sqrt {2} \left (\int _1^x-F(K[1]) K[1]dK[1]+c_1\right )\right )-1-\sqrt {2}\right )}{1+\exp \left (2 \sqrt {2} \left (\int _1^x-F(K[1]) K[1]dK[1]+c_1\right )\right )}\right \}\right \}\] ✓ Maple : cpu = 0.042 (sec), leaf count = 29
dsolve(diff(y(x),x) = -F(x)*(-x^2-2*x*y(x)+y(x)^2)+y(x)/x,y(x))
\[y \left (x \right ) = \frac {x \left (\sqrt {2}+2 \tanh \left (\left (c_{1}+\int F \left (x \right ) x d x \right ) \sqrt {2}\right )\right ) \sqrt {2}}{2}\]