3.584   ODE No. 584

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

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

Mathematica: cpu = 18.981910 (sec), leaf count = 112 $$\text{Solve}[{\int }_1^{y(x)}(\frac{K[2]}{4a^{2}F(K[2{]}^2-4ax)}-\frac{2a{\int }_1^x\frac{K[2]F^{\prime }(K[2{]}^2-4aK[1])}{aF{(K[2{]}^2-4aK[1])}^2}dK[1]-1}{2a})dK[2]+{\int }_1^x-\frac{1}{2aF(y(x{)}^2-4aK[1])}dK[1]=c_1,y(x)]$$

Maple: cpu = 0.047 (sec), leaf count = 35 $$\{\frac{y\left(x\right)}{2a}+\frac{{\int }^{{\left(y\left(x\right)\right)}^2-4ax}{\left(F\left(\mathit{\_}\mathit{a}\right)\right)}^{-1}d\mathit{\_}\mathit{a}}{8a^2}-\mathit{\_}\mathit{C}\mathit{1}=0\}$$