3.587   ODE No. 587

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=1/2(x^{3/2}+2F(y\left(x\right)-1/6x^3))\sqrt{x}=0}}$$

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

Mathematica: cpu = 44.026091 (sec), leaf count = 120 $$\text{Solve}[{\int }_1^{y(x)}-\frac{F(K[2]-\frac{x^3}{6}){\int }_1^x-\frac{K[1{]}^2{F}^{\prime }(K[2]-\frac{K[1{]}^3}{6})}{2F{(K[2]-\frac{K[1{]}^3}{6})}^2}dK[1]+1}{F(K[2]-\frac{x^3}{6})}dK[2]+{\int }_1^x(\frac{K[1{]}^2}{2F(y(x)-\frac{K[1{]}^3}{6})}+\sqrt{K[1]})dK[1]=c_1,y(x)]$$

Maple: cpu = 0.109 (sec), leaf count = 29 $$\{{\int }_{\mathit{\_}\mathit{b}}^{y\left(x\right)}{\left(F(\mathit{\_}\mathit{a}-\frac{x^3}{6})\right)}^{-1}\mathrm{d}\mathit{\_}\mathit{a}-\frac{2}{3}{x}^{\frac{3}{2}}-\mathit{\_}\mathit{C}\mathit{1}=0\}$$