\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {y \left ( x \right ) \left ( \left ( y \left ( x \right ) \right ) ^{2}+y \left ( x \right ) {{\rm e}^{bx}}+ \left ( {{\rm e}^{bx}} \right ) ^{2} \right ) }{ \left ( {{\rm e}^{bx}} \right ) ^{2}}}=0} \]
Mathematica: cpu = 0.163521 (sec), leaf count = 146 \[ \text {Solve}\left [-\frac {1}{3} (9 b-7)^{2/3} \text {RootSum}\left [\text {$\#$1}^3 (9 b-7)^{2/3}-9 \text {$\#$1} b+6 \text {$\#$1}+(9 b-7)^{2/3}\& ,\frac {\log \left (\frac {3 e^{-2 b x} y(x)+e^{-b x}}{\sqrt [3]{(9 b-7) e^{-3 b x}}}-\text {$\#$1}\right )}{\text {$\#$1}^2 \left (-(9 b-7)^{2/3}\right )+3 b-2}\& \right ]=\frac {1}{9} x e^{2 b x} \left ((9 b-7) e^{-3 b x}\right )^{2/3}+c_1,y(x)\right ] \]
Maple: cpu = 0.234 (sec), leaf count = 136 \[ \left \{ y \left ( x \right ) ={\frac {1}{2}\tan \left ( {\it RootOf} \left ( -2\,{\it \_Z}\,{{\rm e}^{bx}}-\ln \left ( -{(4\, \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}b-3\, \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}+4\,b-3) \left ( -\tan \left ( {\it \_Z} \right ) \sqrt {- \left ( {{\rm e}^{bx}} \right ) ^{2} \left ( 4\,b-3 \right ) }+{{\rm e}^{bx}} \right ) ^{-2}} \right ) \sqrt {- \left ( { {\rm e}^{bx}} \right ) ^{2} \left ( 4\,b-3 \right ) }+{\it \_C1}\,\sqrt { - \left ( {{\rm e}^{bx}} \right ) ^{2} \left ( 4\,b-3 \right ) }-2\,x \sqrt {- \left ( {{\rm e}^{bx}} \right ) ^{2} \left ( 4\,b-3 \right ) } \right ) \right ) \sqrt {-{{\rm e}^{2\,bx}} \left ( 4\,b-3 \right ) }}-{ \frac {{{\rm e}^{bx}}}{2}} \right \} \]