2.597   ODE No. 597

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

$$y^{\prime }(x)=\frac{2a}{x^2(2aF\left(\frac{xy(x{)}^2-4a}{x}\right)-y(x))}$$ ✓ Mathematica : cpu = 0.358719 (sec), leaf count = 130

$$\text{Solve}[{\int }_1^{y(x)}(-\frac{K[2]}{2aF\left(\frac{xK[2{]}^2-4a}{x}\right)}-{\int }_1^x\frac{2K[2]F^{\prime }\left(\frac{K[1]K[2{]}^2-4a}{K[1]}\right)}{F{\left(\frac{K[1]K[2{]}^2-4a}{K[1]}\right)}^{2}K[1{]}^2}dK[1]+1)dK[2]+{\int }_1^x-\frac{1}{F\left(\frac{K[1]y(x{)}^2-4a}{K[1]}\right)K[1{]}^2}dK[1]=c_1,y(x)]$$ ✓ Maple : cpu = 0.601 (sec), leaf count = 37

$$\{-\frac{y\left(x\right)}{2a}+\frac{1}{8a^2}{\int }^{{\left(y\left(x\right)\right)}^2-4\frac{a}{x}}{\left(F\left(\mathit{\_}\mathit{a}\right)\right)}^{-1}d\mathit{\_}\mathit{a}-\mathit{\_}\mathit{C}\mathit{1}=0\}$$