\[ y'(x)=\frac {e^x \left (3 e^x-2 y(x)^{3/2}\right )^2}{4 \sqrt {y(x)}} \] ✓ Mathematica : cpu = 0.788413 (sec), leaf count = 222
\[\left \{\left \{y(x)\to \frac {\left (\frac {3}{2} e^{3 c_1+x}+e^{3 c_1}-e^{3 e^x}+\frac {3}{2} e^{x+3 e^x}\right ){}^{2/3}}{\sqrt [3]{\left (e^{3 c_1}+e^{3 e^x}\right ){}^2}}\right \},\left \{y(x)\to -\frac {\sqrt [3]{-1} \left (\frac {3}{2} e^{3 c_1+x}+e^{3 c_1}-e^{3 e^x}+\frac {3}{2} e^{x+3 e^x}\right ){}^{2/3}}{\sqrt [3]{\left (e^{3 c_1}+e^{3 e^x}\right ){}^2}}\right \},\left \{y(x)\to \frac {\left (-\frac {1}{2}\right )^{2/3} \left (3 e^{3 c_1+x}+2 e^{3 c_1}-2 e^{3 e^x}+3 e^{x+3 e^x}\right ){}^{2/3}}{\sqrt [3]{\left (e^{3 c_1}+e^{3 e^x}\right ){}^2}}\right \}\right \}\]
✓ Maple : cpu = 1.24 (sec), leaf count = 72
\[ \left \{ {\it \_C1}+{1{{\rm e}^{-{\frac {3\,{{\rm e}^{x}}}{2}}-{\frac {9\,{{\rm e}^{2\,x}}}{8}}}} \left ( 2\, \left ( y \left ( x \right ) \right ) ^{3/2}{{\rm e}^{x}}-2\,{{\rm e}^{x}}-3\,{{\rm e}^{2\,x}} \right ) \left ( {{\rm e}^{{\frac {3\,{{\rm e}^{x}}}{2}}-{\frac {9\,{{\rm e}^{2\,x}}}{8}}}} \right ) ^{-1} \left ( 2\, \left ( y \left ( x \right ) \right ) ^{3/2}{{\rm e}^{x}}+2\,{{\rm e}^{x}}-3\,{{\rm e}^{2\,x}} \right ) ^{-1}}=0 \right \} \]