2.116   ODE No. 116

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

$$-x\sqrt{(y(x{)}^2-4x^2)(y(x{)}^2-x^2)}+x{y}^{\prime }(x)-y(x)=0$$ ✓ Mathematica : cpu = 0.346476 (sec), leaf count = 121

$$\text{Solve}[\frac{\sqrt{\frac{\frac{y(x)}{x}+2}{\frac{y(x)}{x}-1}}\sqrt{\frac{\frac{y(x)}{x}+1}{\frac{2y(x)}{x}+4}}F({\sin }^{-1}\left(\sqrt{\frac{2}{3}}\sqrt{\frac{\frac{y(x)}{x}-2}{\frac{y(x)}{x}-1}}\right)|\frac{9}{8})}{\sqrt{\frac{\frac{y(x)}{x}+1}{\frac{y(x)}{x}-1}}}=\frac{x^2}{2}+c_1,y(x)]$$ ✓ Maple : cpu = 0.184 (sec), leaf count = 86

$$\{{\int }_{\mathit{\_}\mathit{b}}^x(\mathit{\_}\mathit{a}\sqrt{4{\mathit{\_}\mathit{a}}^4-5{\mathit{\_}\mathit{a}}^2{\left(y\left(x\right)\right)}^2+{\left(y\left(x\right)\right)}^4}+y\left(x\right))\frac{1}{\sqrt{4{\mathit{\_}\mathit{a}}^4-5{\mathit{\_}\mathit{a}}^2{\left(y\left(x\right)\right)}^2+{\left(y\left(x\right)\right)}^4}}\mathrm{d}\mathit{\_}\mathit{a}+{\int }^{y\left(x\right)}-\mathit{\_}\mathit{b}\frac{1}{\sqrt{4{\mathit{\_}\mathit{b}}^4-5{\mathit{\_}\mathit{b}}^2{\mathit{\_}\mathit{f}}^2+{\mathit{\_}\mathit{f}}^4}}d\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1}=0\}$$