2.584   ODE No. 584

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

$$y^{\prime }(x)=\frac{2a}{2aF(y(x{)}^2-4ax)+y(x)}$$ ✓ Mathematica : cpu = 24.2744 (sec), leaf count = 107

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

✓ Maple : cpu = 0.082 (sec), leaf count = 35

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