\[ y'(x)=\frac {y(x)}{x}-F(x) \left (-a y(x)^2-b x^2\right ) \] ✓ Mathematica : cpu = 0.161945 (sec), leaf count = 56
DSolve[Derivative[1][y][x] == y[x]/x - F[x]*(-(b*x^2) - a*y[x]^2),y[x],x]
\[\left \{\left \{y(x)\to \frac {\sqrt {b} x \tan \left (\sqrt {a} \sqrt {b} \int _1^xF(K[1]) K[1]dK[1]+\sqrt {a} \sqrt {b} c_1\right )}{\sqrt {a}}\right \}\right \}\] ✓ Maple : cpu = 0.046 (sec), leaf count = 29
dsolve(diff(y(x),x) = -F(x)*(-a*y(x)^2-b*x^2)+y(x)/x,y(x))
\[y \left (x \right ) = \frac {\tan \left (\sqrt {a b}\, \left (c_{1}+\int F \left (x \right ) x d x \right )\right ) x \sqrt {a b}}{a}\]