3.730   ODE No. 730

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=1/4\frac{{(2{\left(y\left(x\right)\right)}^{3/2}-3{\mathrm{e}}^x)}^3{\mathrm{e}}^x}{(2{\left(y\left(x\right)\right)}^{3/2}-3{\mathrm{e}}^x+2)\sqrt{y\left(x\right)}}=0}}$$

1. Problem in Latex
2. Mathematica input
3. Maple input

Mathematica: cpu = 33.979315 (sec), leaf count = 55 $$\text{DSolve}[y^{\prime }(x)=\frac{e^x{(2y(x{)}^{3/2}-3e^x)}^3}{4\sqrt{y(x)}(2y(x{)}^{3/2}-3e^x+2)},y(x),x]$$

Maple: cpu = 1.342 (sec), leaf count = 49 $$\{{\mathrm{e}}^x-{\int }^{{\left(y\left(x\right)\right)}^{\frac{3}{2}}-\frac{3{\mathrm{e}}^x}{2}}\frac{2\mathit{\_}\mathit{a}}{3{\mathit{\_}\mathit{a}}^3-3\mathit{\_}\mathit{a}-3}+\frac{2}{3{\mathit{\_}\mathit{a}}^3-3\mathit{\_}\mathit{a}-3}d\mathit{\_}\mathit{a}-\mathit{\_}\mathit{C}\mathit{1}=0\}$$