2.494   ODE No. 494

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

$$(y(x{)}^2-a^2{x}^2)y^{\prime }(x{)}^2+(1-a^2)x^2+2xy(x)y^{\prime }(x)=0$$ ✓ Mathematica : cpu = 0.111563 (sec), leaf count = 49

$$\{\{y(x)\to a{c}_1-\sqrt{-x^2+c_1{}^2}\},\{y(x)\to a{c}_1+\sqrt{-x^2+c_1{}^2}\}\}$$ ✓ Maple : cpu = 0.217 (sec), leaf count = 161

$$\{y\left(x\right)=\sqrt{a^2-1}x,y\left(x\right)=\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-\ln \left(x\right)+{\int }^{\mathit{\_}\mathit{Z}}\frac{1}{({\mathit{\_}\mathit{a}}^2+1)({\mathit{\_}\mathit{a}}^2-a^2+1)}(-{\mathit{\_}\mathit{a}}^3+\mathit{\_}\mathit{a}{a}^2+\sqrt{{\mathit{\_}\mathit{a}}^2{a}^2-a^4+a^2}-\mathit{\_}\mathit{a})d\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1})x,y\left(x\right)=\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-\ln \left(x\right)-{\int }^{\mathit{\_}\mathit{Z}}\frac{1}{({\mathit{\_}\mathit{a}}^2+1)({\mathit{\_}\mathit{a}}^2-a^2+1)}({\mathit{\_}\mathit{a}}^3-\mathit{\_}\mathit{a}{a}^2+\sqrt{{\mathit{\_}\mathit{a}}^2{a}^2-a^4+a^2}+\mathit{\_}\mathit{a})d\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1})x,y\left(x\right)=-\sqrt{a^2-1}x\}$$