\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =1/4\,{\frac { \left ( 2\, \left ( y \left ( x \right ) \right ) ^{3/2}-3\,{{\rm e}^{x}} \right ) ^{3}{{\rm e}^{x}}}{ \left ( 2\, \left ( y \left ( x \right ) \right ) ^{3/2}-3\,{{\rm e}^{x}}+2 \right ) \sqrt {y \left ( x \right ) }}}=0} \]
Mathematica: cpu = 33.979315 (sec), leaf count = 55 \[ \text {DSolve}\left [y'(x)=\frac {e^x \left (2 y(x)^{3/2}-3 e^x\right )^3}{4 \sqrt {y(x)} \left (2 y(x)^{3/2}-3 e^x+2\right )},y(x),x\right ] \]
Maple: cpu = 1.342 (sec), leaf count = 49 \[ \left \{ {{\rm e}^{x}}-\int ^{ \left ( y \left ( x \right ) \right ) ^{{ \frac {3}{2}}}-{\frac {3\,{{\rm e}^{x}}}{2}}}\!{\frac {2\,{\it \_a}}{3 \,{{\it \_a}}^{3}-3\,{\it \_a}-3}}+{\frac {2}{3\,{{\it \_a}}^{3}-3\,{ \it \_a}-3}}{d{\it \_a}}-{\it \_C1}=0 \right \} \]