\[ y'(x)=e^{b x} \left (e^{-3 b x} y(x)^3+e^{-2 b x} y(x)^2+1\right ) \] ✓ Mathematica : cpu = 0.302615 (sec), leaf count = 146
\[\text {Solve}\left [-\frac {1}{3} (9 b+29)^{2/3} \text {RootSum}\left [\text {$\#$1}^3 (9 b+29)^{2/3}-9 \text {$\#$1} b-3 \text {$\#$1}+(9 b+29)^{2/3}\& ,\frac {\log \left (\frac {3 e^{-2 b x} y(x)+e^{-b x}}{\sqrt [3]{(9 b+29) e^{-3 b x}}}-\text {$\#$1}\right )}{\text {$\#$1}^2 \left (-(9 b+29)^{2/3}\right )+3 b+1}\& \right ]=\frac {1}{9} x e^{2 b x} \left ((9 b+29) e^{-3 b x}\right )^{2/3}+c_1,y(x)\right ]\] ✓ Maple : cpu = 0.338 (sec), leaf count = 40
\[ \left \{ y \left ( x \right ) ={\frac {1}{{{\rm e}^{-bx}}}{\it RootOf} \left ( -x-\int ^{{\it \_Z}}\!- \left ( {{\it \_a}}^{3}+{{\it \_a}}^{2}-{\it \_a}\,b+1 \right ) ^{-1}{d{\it \_a}}+{\it \_C1} \right ) } \right \} \]