\[ y'(x)=\frac {F(x (y(x)+x))-y(x)-2 x}{x} \] ✓ Mathematica : cpu = 0.283096 (sec), leaf count = 191
DSolve[Derivative[1][y][x] == (-2*x + F[x*(x + y[x])] - y[x])/x,y[x],x]
\[\text {Solve}\left [\int _1^{y(x)}-\frac {x+F(x (x+K[2])) \int _1^x\left (\frac {2 F'(K[1] (K[1]+K[2])) K[1]^2}{F(K[1] (K[1]+K[2]))^2}+\frac {(K[2]-F(K[1] (K[1]+K[2]))) F'(K[1] (K[1]+K[2])) K[1]}{F(K[1] (K[1]+K[2]))^2}-\frac {1-K[1] F'(K[1] (K[1]+K[2]))}{F(K[1] (K[1]+K[2]))}\right )dK[1]}{F(x (x+K[2]))}dK[2]+\int _1^x\left (-\frac {2 K[1]}{F(K[1] (K[1]+y(x)))}-\frac {y(x)-F(K[1] (K[1]+y(x)))}{F(K[1] (K[1]+y(x)))}\right )dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.097 (sec), leaf count = 28
dsolve(diff(y(x),x) = (-2*x-y(x)+F(x*(y(x)+x)))/x,y(x))
\[y \left (x \right ) = \frac {-x^{2}+\RootOf \left (-x +\int _{}^{\textit {\_Z}}\frac {1}{F \left (\textit {\_a} \right )}d \textit {\_a} +c_{1}\right )}{x}\]