2.604   ODE No. 604

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

$$y^{\prime }(x)=\frac{2y(x{)}^3}{2y(x)F\left(\frac{4xy(x{)}^2+1}{y(x{)}^2}\right)+1}$$ ✓ Mathematica : cpu = 0.378156 (sec), leaf count = 143

$$\text{Solve}[{\int }_1^{y(x)}(-{\int }_1^x\frac{(\frac{8K[1]}{K[2]}-\frac{2(4K[1]K[2{]}^2+1)}{K[2{]}^3})F^{\prime }\left(\frac{4K[1]K[2{]}^2+1}{K[2{]}^2}\right)}{F{\left(\frac{4K[1]K[2{]}^2+1}{K[2{]}^2}\right)}^2}dK[1]+\frac{1}{K[2{]}^2}+\frac{1}{2F\left(\frac{4xK[2{]}^2+1}{K[2{]}^2}\right)K[2{]}^3})dK[2]+{\int }_1^x-\frac{1}{F\left(\frac{4K[1]y(x{)}^2+1}{y(x{)}^2}\right)}dK[1]=c_1,y(x)]$$ ✓ Maple : cpu = 0.176 (sec), leaf count = 30

$$\{-\mathit{\_}\mathit{C}\mathit{1}-{\left(y\left(x\right)\right)}^{-1}-\frac{{\int }^{4x+{\left(y\left(x\right)\right)}^{-2}}{\left(F\left(\mathit{\_}\mathit{a}\right)\right)}^{-1}d\mathit{\_}\mathit{a}}{4}=0\}$$