3.582   ODE No. 582

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=\frac{1}{a{x}^2}(1+F\left(\frac{axy\left(x\right)+1}{ax}\right)a{x}^2)=0}}$$

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

Mathematica: cpu = 16.699621 (sec), leaf count = 139 $$\text{Solve}[{\int }_1^{y(x)}-\frac{F\left(\frac{axK[2]+1}{ax}\right){\int }_1^x\frac{F^{\prime }\left(\frac{aK[1]K[2]+1}{aK[1]}\right)}{aK[1{]}^{2}F{\left(\frac{aK[1]K[2]+1}{aK[1]}\right)}^2}dK[1]-1}{F\left(\frac{axK[2]+1}{ax}\right)}dK[2]+{\int }_1^x(-\frac{1}{aK[1{]}^{2}F\left(\frac{ay(x)K[1]+1}{aK[1]}\right)}-1)dK[1]=c_1,y(x)]$$

Maple: cpu = 0.156 (sec), leaf count = 30 $$\{y\left(x\right)=\frac{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-x+{\int }^{\mathit{\_}\mathit{Z}}{\left(F\left(\mathit{\_}\mathit{a}\right)\right)}^{-1}d\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1})ax-1}{ax}\}$$