\[ y'(x)=\frac {e^x \left (3 e^x-2 y(x)^{3/2}\right )^2}{4 \sqrt {y(x)}} \] ✓ Mathematica : cpu = 0.710669 (sec), leaf count = 264
\[\left \{\left \{y(x)\to \frac {\left (-2 e^{3 e^x}+3 e^{x+3 e^x}+3 e^{x+3 c_1}+2 e^{3 c_1}\right ){}^{2/3}}{\sqrt [3]{4 e^{6 e^x}+8 e^{3 e^x+3 c_1}+4 e^{6 c_1}}}\right \},\left \{y(x)\to -\frac {\sqrt [3]{-1} \left (-2 e^{3 e^x}+3 e^{x+3 e^x}+3 e^{x+3 c_1}+2 e^{3 c_1}\right ){}^{2/3}}{\sqrt [3]{4 e^{6 e^x}+8 e^{3 e^x+3 c_1}+4 e^{6 c_1}}}\right \},\left \{y(x)\to \frac {(-1)^{2/3} \left (-2 e^{3 e^x}+3 e^{x+3 e^x}+3 e^{x+3 c_1}+2 e^{3 c_1}\right ){}^{2/3}}{\sqrt [3]{4 e^{6 e^x}+8 e^{3 e^x+3 c_1}+4 e^{6 c_1}}}\right \}\right \}\] ✓ Maple : cpu = 0.505 (sec), leaf count = 72
\[ \left \{ {\it \_C1}+{{{\rm e}^{-{\frac {3\,{{\rm e}^{x}}}{2}}-{\frac {9\,{{\rm e}^{2\,x}}}{8}}}} \left ( 2\, \left ( y \left ( x \right ) \right ) ^{3/2}{{\rm e}^{x}}-2\,{{\rm e}^{x}}-3\,{{\rm e}^{2\,x}} \right ) \left ( {{\rm e}^{{\frac {3\,{{\rm e}^{x}}}{2}}-{\frac {9\,{{\rm e}^{2\,x}}}{8}}}} \right ) ^{-1} \left ( 2\, \left ( y \left ( x \right ) \right ) ^{3/2}{{\rm e}^{x}}+2\,{{\rm e}^{x}}-3\,{{\rm e}^{2\,x}} \right ) ^{-1}}=0 \right \} \]