\[ y'(x)=\frac {2 x F(y(x)+\log (2 x+1))+F(y(x)+\log (2 x+1))-2}{2 x+1} \] ✓ Mathematica : cpu = 0.315651 (sec), leaf count = 117
\[\text {Solve}\left [\int _1^{y(x)}-\frac {F(K[2]+\log (2 x+1)) \int _1^x-\frac {2 F'(K[2]+\log (2 K[1]+1))}{F(K[2]+\log (2 K[1]+1))^2 (2 K[1]+1)}dK[1]-1}{F(K[2]+\log (2 x+1))}dK[2]+\int _1^x\left (\frac {2}{F(\log (2 K[1]+1)+y(x)) (2 K[1]+1)}-1\right )dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.24 (sec), leaf count = 27
\[ \left \{ y \left ( x \right ) =-\ln \left ( 2\,x+1 \right ) +{\it RootOf} \left ( -x+\int ^{{\it \_Z}}\! \left ( F \left ( {\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}+{\it \_C1} \right ) \right \} \]