\[ y'(x)=\frac {e^x \left (3 e^x-2 y(x)^{3/2}\right )^2}{4 \sqrt {y(x)}} \] ✓ Mathematica : cpu = 0.712139 (sec), leaf count = 264
DSolve[Derivative[1][y][x] == (E^x*(3*E^x - 2*y[x]^(3/2))^2)/(4*Sqrt[y[x]]),y[x],x]
\[\left \{\left \{y(x)\to \frac {\left (-2 e^{3 e^x}+3 e^{x+3 e^x}+3 e^{x+3 c_1}+2 e^{3 c_1}\right ){}^{2/3}}{\sqrt [3]{4 e^{6 e^x}+8 e^{3 e^x+3 c_1}+4 e^{6 c_1}}}\right \},\left \{y(x)\to -\frac {\sqrt [3]{-1} \left (-2 e^{3 e^x}+3 e^{x+3 e^x}+3 e^{x+3 c_1}+2 e^{3 c_1}\right ){}^{2/3}}{\sqrt [3]{4 e^{6 e^x}+8 e^{3 e^x+3 c_1}+4 e^{6 c_1}}}\right \},\left \{y(x)\to \frac {(-1)^{2/3} \left (-2 e^{3 e^x}+3 e^{x+3 e^x}+3 e^{x+3 c_1}+2 e^{3 c_1}\right ){}^{2/3}}{\sqrt [3]{4 e^{6 e^x}+8 e^{3 e^x+3 c_1}+4 e^{6 c_1}}}\right \}\right \}\] ✓ Maple : cpu = 0.19 (sec), leaf count = 72
dsolve(diff(y(x),x) = 1/4*(-2*y(x)^(3/2)+3*exp(x))^2*exp(x)/y(x)^(1/2),y(x))
\[c_{1}+\frac {{\mathrm e}^{-\frac {3 \,{\mathrm e}^{x}}{2}-\frac {9 \,{\mathrm e}^{2 x}}{8}} \left (2 y \left (x \right )^{\frac {3}{2}} {\mathrm e}^{x}-2 \,{\mathrm e}^{x}-3 \,{\mathrm e}^{2 x}\right ) {\mathrm e}^{-\frac {3 \,{\mathrm e}^{x}}{2}+\frac {9 \,{\mathrm e}^{2 x}}{8}}}{2 y \left (x \right )^{\frac {3}{2}} {\mathrm e}^{x}+2 \,{\mathrm e}^{x}-3 \,{\mathrm e}^{2 x}} = 0\]