\[ y'(x)=\frac {e^x \left (2 y(x)^{3/2}-3 e^x\right )^3}{4 \sqrt {y(x)} \left (2 y(x)^{3/2}-3 e^x+2\right )} \] ✓ Mathematica : cpu = 0.308546 (sec), leaf count = 83
DSolve[Derivative[1][y][x] == (E^x*(-3*E^x + 2*y[x]^(3/2))^3)/(4*Sqrt[y[x]]*(2 - 3*E^x + 2*y[x]^(3/2))),y[x],x]
\[\text {Solve}\left [-\frac {2}{3} \text {RootSum}\left [\text {$\#$1}^3-\text {$\#$1}-1\& ,\frac {\text {$\#$1} \log \left (-\text {$\#$1}+y(x)^{3/2}-\frac {3 e^x}{2}\right )+\log \left (-\text {$\#$1}+y(x)^{3/2}-\frac {3 e^x}{2}\right )}{3 \text {$\#$1}^2-1}\& \right ]+e^x-c_1=0,y(x)\right ]\] ✓ Maple : cpu = 1.582 (sec), leaf count = 41
dsolve(diff(y(x),x) = 1/4*(2*y(x)^(3/2)-3*exp(x))^3*exp(x)/(2*y(x)^(3/2)-3*exp(x)+2)/y(x)^(1/2),y(x))
\[{\mathrm e}^{x}-\left (\int _{}^{y \left (x \right )^{\frac {3}{2}}-\frac {3 \,{\mathrm e}^{x}}{2}}\frac {2+2 \textit {\_a}}{3 \textit {\_a}^{3}-3 \textit {\_a} -3}d \textit {\_a} \right )-c_{1} = 0\]