\[ y'(x)=-\frac {e^x \left (-8 y(x)^{9/2}+36 e^x y(x)^3-8 y(x)^3+24 e^x y(x)^{3/2}-54 e^{2 x} y(x)^{3/2}-18 e^{2 x}+27 e^{3 x}-8\right )}{8 \sqrt {y(x)}} \] ✓ Mathematica : cpu = 1.50614 (sec), leaf count = 68
\[\text {Solve}\left [\frac {2}{3} \log \left (y(x)^{3/2}-\frac {3 e^x}{2}\right )+e^x=\frac {4}{9 e^x-6 y(x)^{3/2}}+\frac {2}{3} \log \left (y(x)^{3/2}-\frac {3 e^x}{2}+1\right )+c_1,y(x)\right ]\] ✓ Maple : cpu = 0.864 (sec), leaf count = 49
\[{\mathrm e}^{x}-\frac {4}{-6 y \relax (x )^{\frac {3}{2}}+9 \,{\mathrm e}^{x}}+\frac {2 \ln \left (y \relax (x )^{\frac {3}{2}}-\frac {3 \,{\mathrm e}^{x}}{2}\right )}{3}-\frac {2 \ln \left (y \relax (x )^{\frac {3}{2}}-\frac {3 \,{\mathrm e}^{x}}{2}+1\right )}{3}-c_{1} = 0\]