\[ y'(x)=e^{b x} F\left (e^{-b x} y(x)\right ) \] ✓ Mathematica : cpu = 0.330247 (sec), leaf count = 203
\[\text {Solve}\left [\int _1^{y(x)}\left (\frac {1}{b K[2]-e^{b x} F\left (e^{-b x} K[2]\right )}-\int _1^x\left (\frac {F'\left (e^{-b K[1]} K[2]\right )}{e^{b K[1]} F\left (e^{-b K[1]} K[2]\right )-b K[2]}-\frac {e^{b K[1]} F\left (e^{-b K[1]} K[2]\right ) \left (F'\left (e^{-b K[1]} K[2]\right )-b\right )}{\left (e^{b K[1]} F\left (e^{-b K[1]} K[2]\right )-b K[2]\right )^2}\right )dK[1]\right )dK[2]+\int _1^x\frac {e^{b K[1]} F\left (e^{-b K[1]} y(x)\right )}{e^{b K[1]} F\left (e^{-b K[1]} y(x)\right )-b y(x)}dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.07 (sec), leaf count = 31
\[\left \{y \left (x \right ) = \RootOf \left (c_{1}-x +\int _{}^{\textit {\_Z}}\frac {1}{-\textit {\_a} b +F \left (\textit {\_a} \right )}d \textit {\_a} \right ) {\mathrm e}^{b x}\right \}\]