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 = 36.2004 (sec), leaf count = 112

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

✓ Maple : cpu = 0.453 (sec), leaf count = 37

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