\[ y'(x)=e^{-2 b x} y(x) \left (e^{b x} y(x)+e^{2 b x}+y(x)^2\right ) \] ✓ Mathematica : cpu = 0.406176 (sec), leaf count = 146
DSolve[Derivative[1][y][x] == (y[x]*(E^(2*b*x) + E^(b*x)*y[x] + y[x]^2))/E^(2*b*x),y[x],x]
\[\text {Solve}\left [-\frac {1}{3} (9 b-7)^{2/3} \text {RootSum}\left [\text {$\#$1}^3 (9 b-7)^{2/3}-9 \text {$\#$1} b+6 \text {$\#$1}+(9 b-7)^{2/3}\& ,\frac {\log \left (\frac {3 e^{-2 b x} y(x)+e^{-b x}}{\sqrt [3]{(9 b-7) e^{-3 b x}}}-\text {$\#$1}\right )}{\text {$\#$1}^2 \left (-(9 b-7)^{2/3}\right )+3 b-2}\& \right ]=\frac {1}{9} x e^{2 b x} \left ((9 b-7) e^{-3 b x}\right )^{2/3}+c_1,y(x)\right ]\] ✓ Maple : cpu = 0.37 (sec), leaf count = 134
dsolve(diff(y(x),x) = y(x)*(y(x)^2+y(x)*exp(b*x)+exp(b*x)^2)/exp(b*x)^2,y(x))
\[y \left (x \right ) = -\frac {\tan \left (\RootOf \left (-\ln \left (\frac {4 \left (\tan ^{2}\left (\textit {\_Z} \right )\right ) b -3 \left (\tan ^{2}\left (\textit {\_Z} \right )\right )+4 b -3}{\left (\tan \left (\textit {\_Z} \right ) \sqrt {-{\mathrm e}^{2 b x} \left (4 b -3\right )}+{\mathrm e}^{b x}\right )^{2}}\right ) \sqrt {-{\mathrm e}^{2 b x} \left (4 b -3\right )}+c_{1} \sqrt {-{\mathrm e}^{2 b x} \left (4 b -3\right )}-2 x \sqrt {-{\mathrm e}^{2 b x} \left (4 b -3\right )}+2 \textit {\_Z} \,{\mathrm e}^{b x}\right )\right ) \sqrt {\left (-4 b +3\right ) {\mathrm e}^{2 b x}}}{2}-\frac {{\mathrm e}^{b x}}{2}\]