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 = 0.456118 (sec), leaf count = 253

$$\text{Solve}[{\int }_1^{y(x)}(-\frac{bK[2]}{b+\sqrt{a}F\left(\frac{b{x}^2+aK[2{]}^2}{a}\right)}-{\int }_1^x(\frac{2bK[1]K[2]F^{\prime }\left(\frac{bK[1{]}^2+aK[2{]}^2}{a}\right)}{\sqrt{a}(b+\sqrt{a}F\left(\frac{bK[1{]}^2+aK[2{]}^2}{a}\right))}-\frac{2bF\left(\frac{bK[1{]}^2+aK[2{]}^2}{a}\right)K[1]K[2]F^{\prime }\left(\frac{bK[1{]}^2+aK[2{]}^2}{a}\right)}{{(b+\sqrt{a}F\left(\frac{bK[1{]}^2+aK[2{]}^2}{a}\right))}^2})dK[1])dK[2]+{\int }_1^x\frac{bF\left(\frac{bK[1{]}^2+ay(x{)}^2}{a}\right)K[1]}{\sqrt{a}(b+\sqrt{a}F\left(\frac{bK[1{]}^2+ay(x{)}^2}{a}\right))}dK[1]=c_1,y(x)]$$ ✓ Maple : cpu = 0.565 (sec), leaf count = 108

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