2.616   ODE No. 616

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

$$y^{\prime }(x)=\frac{F(x(xy(x)-1))-2x^{3}y(x)+x^2}{x^4}$$ ✓ Mathematica : cpu = 45.5148 (sec), leaf count = 174

$$\text{Solve}[{\int }_1^{y(x)}-\frac{F(x(xK[2]-1)){\int }_1^x(\frac{2K[2]K[1{]}^3{F}^{\prime }(K[1](K[1]K[2]-1))}{F(K[1](K[1]K[2]-1){)}^2}-\frac{K[1{]}^2{F}^{\prime }(K[1](K[1]K[2]-1))}{F(K[1](K[1]K[2]-1){)}^2}-\frac{2K[1]}{F(K[1](K[1]K[2]-1))})dK[1]+x^2}{F(x(xK[2]-1))}dK[2]+{\int }_1^x(-\frac{2y(x)K[1]}{F(K[1](y(x)K[1]-1))}+\frac{1}{F(K[1](y(x)K[1]-1))}+\frac{1}{K[1{]}^2})dK[1]=c_1,y(x)]$$

✓ Maple : cpu = 0.1 (sec), leaf count = 26

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