3.597   ODE No. 597

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=2\frac{a}{x^2}{(-y\left(x\right)+2F\left(\frac{x{\left(y\left(x\right)\right)}^2-4a}{x}\right)a)}^{-1}=0}}$$

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

Mathematica: cpu = 27.163949 (sec), leaf count = 127 $$\text{Solve}[{\int }_1^{y(x)}(-{\int }_1^x\frac{2K[2]F^{\prime }\left(\frac{K[1]K[2{]}^2-4a}{K[1]}\right)}{K[1{]}^{2}F{\left(\frac{K[1]K[2{]}^2-4a}{K[1]}\right)}^2}dK[1]-\frac{K[2]}{2aF\left(\frac{xK[2{]}^2-4a}{x}\right)}+1)dK[2]+{\int }_1^x-\frac{1}{K[1{]}^{2}F\left(\frac{y(x{)}^{2}K[1]-4a}{K[1]}\right)}dK[1]=c_1,y(x)]$$

Maple: cpu = 0.296 (sec), leaf count = 37 $$\{-\frac{y\left(x\right)}{2a}+\frac{1}{8a^2}{\int }^{{\left(y\left(x\right)\right)}^2-4\frac{a}{x}}{\left(F\left(\mathit{\_}\mathit{a}\right)\right)}^{-1}d\mathit{\_}\mathit{a}-\mathit{\_}\mathit{C}\mathit{1}=0\}$$