\[ y'(x)=\frac {y(x)}{x}-F(x) \left (y(x)^2-a x^2\right ) \] ✓ Mathematica : cpu = 0.107244 (sec), leaf count = 41
DSolve[Derivative[1][y][x] == y[x]/x - F[x]*(-(a*x^2) + y[x]^2),y[x],x]
\[\left \{\left \{y(x)\to \sqrt {a} x \tanh \left (\sqrt {a} \int _1^xF(K[1]) K[1]dK[1]+\sqrt {a} c_1\right )\right \}\right \}\] ✓ Maple : cpu = 0.045 (sec), leaf count = 22
dsolve(diff(y(x),x) = -F(x)*(-a*x^2+y(x)^2)+y(x)/x,y(x))
\[y \left (x \right ) = \tanh \left (\sqrt {a}\, \left (c_{1}+\int F \left (x \right ) x d x \right )\right ) x \sqrt {a}\]