2.582   ODE No. 582

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

$$y^{\prime }(x)=\frac{a{x}^{2}F\left(\frac{axy(x)+1}{ax}\right)+1}{a{x}^2}$$ ✓ Mathematica : cpu = 0.258947 (sec), leaf count = 142

$$\text{Solve}[{\int }_1^{y(x)}-\frac{F\left(\frac{axK[2]+1}{ax}\right){\int }_1^x\frac{F^{\prime }\left(\frac{aK[1]K[2]+1}{aK[1]}\right)}{aF{\left(\frac{aK[1]K[2]+1}{aK[1]}\right)}^{2}K[1{]}^2}dK[1]-1}{F\left(\frac{axK[2]+1}{ax}\right)}dK[2]+{\int }_1^x(-1-\frac{1}{aK[1{]}^{2}F\left(\frac{aK[1]y(x)+1}{aK[1]}\right)})dK[1]=c_1,y(x)]$$ ✓ Maple : cpu = 0.28 (sec), leaf count = 30

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