2.605   ODE No. 605

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

$$y^{\prime }(x)=-\frac{y(x{)}^2(2x-F\left(\frac{1-\frac{1}{2}xy(x)}{y(x)}\right))}{4x}$$ ✓ Mathematica : cpu = 0.450136 (sec), leaf count = 145

$$\text{Solve}[{\int }_1^{y(x)}(-{\int }_1^x\frac{2(-\frac{K[1]}{2K[2]}-\frac{1-\frac{1}{2}K[1]K[2]}{K[2{]}^2})F^{\prime }\left(\frac{1-\frac{1}{2}K[1]K[2]}{K[2]}\right)}{F{\left(\frac{1-\frac{1}{2}K[1]K[2]}{K[2]}\right)}^2}dK[1]-\frac{4}{F\left(\frac{1-\frac{1}{2}xK[2]}{K[2]}\right)K[2{]}^2})dK[2]+{\int }_1^x(\frac{1}{K[1]}-\frac{2}{F\left(\frac{1-\frac{1}{2}K[1]y(x)}{y(x)}\right)})dK[1]=c_1,y(x)]$$ ✓ Maple : cpu = 0.295 (sec), leaf count = 29

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