3.593   ODE No. 593

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

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

Mathematica: cpu = 62.104386 (sec), leaf count = 218 $$\text{Solve}[{\int }_1^{y(x)}(\frac{\sqrt{K[2]}}{F(K[2{]}^{3/2}-\frac{3e^x}{2})-1}-{\int }_1^x(\frac{3e^{K[1]}\sqrt{K[2]}F(K[2{]}^{3/2}-\frac{3e^{K[1]}}{2})F^{\prime }(K[2{]}^{3/2}-\frac{3e^{K[1]}}{2})}{2{(F(K[2{]}^{3/2}-\frac{3e^{K[1]}}{2})-1)}^2}-\frac{3e^{K[1]}\sqrt{K[2]}{F}^{\prime }(K[2{]}^{3/2}-\frac{3e^{K[1]}}{2})}{2(F(K[2{]}^{3/2}-\frac{3e^{K[1]}}{2})-1)})dK[1])dK[2]+{\int }_1^x-\frac{e^{K[1]}F(y(x{)}^{3/2}-\frac{3e^{K[1]}}{2})}{F(y(x{)}^{3/2}-\frac{3e^{K[1]}}{2})-1}dK[1]=c_1,y(x)]$$

Maple: cpu = 0.265 (sec), leaf count = 35 $$\{{\int }_{\mathit{\_}\mathit{b}}^{y\left(x\right)}1\sqrt{\mathit{\_}\mathit{a}}{(F({\mathit{\_}\mathit{a}}^{\frac{3}{2}}-\frac{3{\mathrm{e}}^x}{2})-1)}^{-1}\mathrm{d}\mathit{\_}\mathit{a}-{\mathrm{e}}^x-\mathit{\_}\mathit{C}\mathit{1}=0\}$$