\[ y'(x)=\frac {2 y(x)^3}{2 y(x) F\left (\frac {4 x y(x)^2+1}{y(x)^2}\right )+1} \] ✓ Mathematica : cpu = 0.381232 (sec), leaf count = 143
DSolve[Derivative[1][y][x] == (2*y[x]^3)/(1 + 2*F[(1 + 4*x*y[x]^2)/y[x]^2]*y[x]),y[x],x]
\[\text {Solve}\left [\int _1^{y(x)}\left (-\int _1^x\frac {\left (\frac {8 K[1]}{K[2]}-\frac {2 \left (4 K[1] K[2]^2+1\right )}{K[2]^3}\right ) F'\left (\frac {4 K[1] K[2]^2+1}{K[2]^2}\right )}{F\left (\frac {4 K[1] K[2]^2+1}{K[2]^2}\right )^2}dK[1]+\frac {1}{K[2]^2}+\frac {1}{2 F\left (\frac {4 x K[2]^2+1}{K[2]^2}\right ) K[2]^3}\right )dK[2]+\int _1^x-\frac {1}{F\left (\frac {4 K[1] y(x)^2+1}{y(x)^2}\right )}dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.122 (sec), leaf count = 30
dsolve(diff(y(x),x) = 2*y(x)^3/(1+2*F((1+4*x*y(x)^2)/y(x)^2)*y(x)),y(x))
\[-c_{1}-\frac {1}{y \left (x \right )}-\frac {\left (\int _{}^{4 x +\frac {1}{y \left (x \right )^{2}}}\frac {1}{F \left (\textit {\_a} \right )}d \textit {\_a} \right )}{4} = 0\]