\[ y'(x)=e^{b x} F\left (e^{-b x} y(x)\right ) \] ✓ Mathematica : cpu = 0.295867 (sec), leaf count = 203
DSolve[Derivative[1][y][x] == E^(b*x)*F[y[x]/E^(b*x)],y[x],x]
\[\text {Solve}\left [\int _1^{y(x)}\left (\frac {1}{b K[2]-e^{b x} F\left (e^{-b x} K[2]\right )}-\int _1^x\left (\frac {F'\left (e^{-b K[1]} K[2]\right )}{e^{b K[1]} F\left (e^{-b K[1]} K[2]\right )-b K[2]}-\frac {e^{b K[1]} F\left (e^{-b K[1]} K[2]\right ) \left (F'\left (e^{-b K[1]} K[2]\right )-b\right )}{\left (e^{b K[1]} F\left (e^{-b K[1]} K[2]\right )-b K[2]\right )^2}\right )dK[1]\right )dK[2]+\int _1^x\frac {e^{b K[1]} F\left (e^{-b K[1]} y(x)\right )}{e^{b K[1]} F\left (e^{-b K[1]} y(x)\right )-b y(x)}dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.075 (sec), leaf count = 31
dsolve(diff(y(x),x) = F(y(x)*exp(-b*x))*exp(b*x),y(x))
\[y \left (x \right ) = \RootOf \left (-x +\int _{}^{\textit {\_Z}}\frac {1}{F \left (\textit {\_a} \right )-\textit {\_a} b}d \textit {\_a} +c_{1}\right ) {\mathrm e}^{b x}\]