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