\[ y'(x)=\frac {x^3 F\left (\frac {y(x)}{x^2}\right )+2 y(x)}{x} \] ✓ Mathematica : cpu = 0.233257 (sec), leaf count = 121
DSolve[Derivative[1][y][x] == (x^3*F[y[x]/x^2] + 2*y[x])/x,y[x],x]
\[\text {Solve}\left [\int _1^{y(x)}-\frac {F\left (\frac {K[2]}{x^2}\right ) \int _1^x\left (\frac {2}{F\left (\frac {K[2]}{K[1]^2}\right ) K[1]^3}-\frac {2 K[2] F'\left (\frac {K[2]}{K[1]^2}\right )}{F\left (\frac {K[2]}{K[1]^2}\right )^2 K[1]^5}\right )dK[1] x^2+1}{x^2 F\left (\frac {K[2]}{x^2}\right )}dK[2]+\int _1^x\left (\frac {2 y(x)}{F\left (\frac {y(x)}{K[1]^2}\right ) K[1]^3}+1\right )dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.11 (sec), leaf count = 22
dsolve(diff(y(x),x) = (2*y(x)+F(1/x^2*y(x))*x^3)/x,y(x))
\[y \left (x \right ) = \RootOf \left (-x +\int _{}^{\textit {\_Z}}\frac {1}{F \left (\textit {\_a} \right )}d \textit {\_a} +c_{1}\right ) x^{2}\]