2.581   ODE No. 581

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

$$y^{\prime }(x)=\frac{xF\left(\frac{x^{2}y(x)+\frac{1}{4}}{x^2}\right)+\frac{1}{2}}{x^3}$$ ✓ Mathematica : cpu = 38.9149 (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 = 0.104 (sec), leaf count = 32

$$\{y\left(x\right)=\frac{4\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}({\int }^{\mathit{\_}\mathit{Z}}{\left(F\left(\mathit{\_}\mathit{a}\right)\right)}^{-1}d\mathit{\_}\mathit{a}x+x\mathit{\_}\mathit{C}\mathit{1}+1)x^2-1}{4x^2}\}$$