3.581   ODE No. 581

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

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

Mathematica: cpu = 40.986705 (sec), leaf count = 141 $$\text{Solve}[{\int }_1^{y(x)}-\frac{F\left(\frac{x^{2}K[2]+\frac{1}{4}}{x^2}\right){\int }_1^x-\frac{F^{\prime }\left(\frac{K[2]K[1{]}^2+\frac{1}{4}}{K[1{]}^2}\right)}{2K[1{]}^{3}F{\left(\frac{K[2]K[1{]}^2+\frac{1}{4}}{K[1{]}^2}\right)}^2}dK[1]+1}{F\left(\frac{x^{2}K[2]+\frac{1}{4}}{x^2}\right)}dK[2]+{\int }_1^x(\frac{1}{2K[1{]}^{3}F\left(\frac{y(x)K[1{]}^2+\frac{1}{4}}{K[1{]}^2}\right)}+\frac{1}{K[1{]}^2})dK[1]=c_1,y(x)]$$

Maple: cpu = 0.093 (sec), leaf count = 32 $$\{y\left(x\right)=\frac{4\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}({\int }^{\mathit{\_}\mathit{Z}}{\left(F\left(\mathit{\_}\mathit{a}\right)\right)}^{-1}d\mathit{\_}\mathit{a}x+\mathit{\_}\mathit{C}\mathit{1}x+1)x^2-1}{4x^2}\}$$