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 = 0.233556 (sec), leaf count = 144

$$\text{Solve}[{\int }_1^{y(x)}-\frac{F\left(\frac{K[2]x^2+\frac{1}{4}}{x^2}\right){\int }_1^x-\frac{F^{\prime }\left(\frac{K[2]K[1{]}^2+\frac{1}{4}}{K[1{]}^2}\right)}{2F{\left(\frac{K[2]K[1{]}^2+\frac{1}{4}}{K[1{]}^2}\right)}^{2}K[1{]}^3}dK[1]+1}{F\left(\frac{K[2]x^2+\frac{1}{4}}{x^2}\right)}dK[2]+{\int }_1^x(\frac{1}{K[1{]}^2}+\frac{1}{2K[1{]}^{3}F\left(\frac{y(x)K[1{]}^2+\frac{1}{4}}{K[1{]}^2}\right)})dK[1]=c_1,y(x)]$$ ✓ Maple : cpu = 0.216 (sec), leaf count = 32

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