2.591   ODE No. 591

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

$$y^{\prime }(x)=\frac{xF\left(\frac{ay(x{)}^2+b{x}^2}{a}\right)}{\sqrt{a}y(x)}$$ ✓ Mathematica : cpu = 26.7633 (sec), leaf count = 160

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

✓ Maple : cpu = 0.219 (sec), leaf count = 108

$$\{y\left(x\right)=\frac{1}{a}\sqrt{a(-b{x}^2+\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}({\int }^{\mathit{\_}\mathit{Z}}{(F\left(\mathit{\_}\mathit{a}\right)a+b\sqrt{a})}^{-1}d\mathit{\_}\mathit{a}b{a}^{\frac{3}{2}}-b{x}^2+2\mathit{\_}\mathit{C}\mathit{1}a)a)},y\left(x\right)=-\frac{1}{a}\sqrt{a(-b{x}^2+\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}({\int }^{\mathit{\_}\mathit{Z}}{(F\left(\mathit{\_}\mathit{a}\right)a+b\sqrt{a})}^{-1}d\mathit{\_}\mathit{a}b{a}^{\frac{3}{2}}-b{x}^2+2\mathit{\_}\mathit{C}\mathit{1}a)a)}\}$$