\[ y'(x)=\frac {e^x F\left (y(x)^{3/2}-\frac {3 e^x}{2}\right )}{\sqrt {y(x)}} \] ✓ Mathematica : cpu = 0.408659 (sec), leaf count = 221
\[\text {Solve}\left [\int _1^{y(x)}\left (\frac {\sqrt {K[2]}}{F\left (K[2]^{3/2}-\frac {3 e^x}{2}\right )-1}-\int _1^x\left (\frac {3 e^{K[1]} F\left (K[2]^{3/2}-\frac {3 e^{K[1]}}{2}\right ) \sqrt {K[2]} F'\left (K[2]^{3/2}-\frac {3 e^{K[1]}}{2}\right )}{2 \left (F\left (K[2]^{3/2}-\frac {3 e^{K[1]}}{2}\right )-1\right )^2}-\frac {3 e^{K[1]} \sqrt {K[2]} F'\left (K[2]^{3/2}-\frac {3 e^{K[1]}}{2}\right )}{2 \left (F\left (K[2]^{3/2}-\frac {3 e^{K[1]}}{2}\right )-1\right )}\right )dK[1]\right )dK[2]+\int _1^x-\frac {e^{K[1]} F\left (y(x)^{3/2}-\frac {3 e^{K[1]}}{2}\right )}{F\left (y(x)^{3/2}-\frac {3 e^{K[1]}}{2}\right )-1}dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.308 (sec), leaf count = 35
\[\int _{\textit {\_b}}^{y \relax (x )}\frac {\sqrt {\textit {\_a}}}{F \left (\textit {\_a}^{\frac {3}{2}}-\frac {3 \,{\mathrm e}^{x}}{2}\right )-1}d \textit {\_a} -{\mathrm e}^{x}-c_{1} = 0\]