\[ y'(x)=e^{b x} F\left (e^{-b x} y(x)\right ) \] ✓ Mathematica : cpu = 31.8126 (sec), leaf count = 161
\[\text {Solve}\left [c_1=\int _1^{y(x)} \left (\frac {1}{b K[2]-e^{b x} F\left (e^{-b x} K[2]\right )}-\int _1^x \frac {b \left (e^{b K[1]} F\left (K[2] e^{-b K[1]}\right )-K[2] F'\left (K[2] e^{-b K[1]}\right )\right )}{\left (e^{b K[1]} F\left (K[2] e^{-b K[1]}\right )-b K[2]\right )^2} \, dK[1]\right ) \, dK[2]+\int _1^x \frac {e^{b K[1]} F\left (y(x) e^{-b K[1]}\right )}{e^{b K[1]} F\left (y(x) e^{-b K[1]}\right )-b y(x)} \, dK[1],y(x)\right ]\]
✓ Maple : cpu = 0.504 (sec), leaf count = 31
\[ \left \{ y \left ( x \right ) ={\frac {{\it RootOf} \left ( -x+\int ^{{\it \_Z}}\! \left ( F \left ( {\it \_a} \right ) -{\it \_a}\,b \right ) ^{-1}{d{\it \_a}}+{\it \_C1} \right ) }{{{\rm e}^{-bx}}}} \right \} \]