3.494   ODE No. 494

$$\boxed{{\displaystyle ({\left(y\left(x\right)\right)}^2-a^2{x}^2){\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2+2xy\left(x\right)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+(-a^2+1)x^2=0}}$$

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

Mathematica: cpu = 0 (sec), leaf count = 0 $$\text{Hanged}$$

Maple: cpu = 0.764 (sec), leaf count = 173 $$\{y\left(x\right)=\sqrt{a^2-1}x,y\left(x\right)=\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-\ln \left(x\right)+{\int }^{\mathit{\_}\mathit{Z}}\frac{1}{{\mathit{\_}\mathit{a}}^4-{\mathit{\_}\mathit{a}}^2{a}^2+2{\mathit{\_}\mathit{a}}^2-a^2+1}(-{\mathit{\_}\mathit{a}}^3+\mathit{\_}\mathit{a}{a}^2+\sqrt{{\mathit{\_}\mathit{a}}^2{a}^2-a^4+a^2}-\mathit{\_}\mathit{a})d\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1})x,y\left(x\right)=\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-\ln \left(x\right)-{\int }^{\mathit{\_}\mathit{Z}}\frac{1}{{\mathit{\_}\mathit{a}}^4-{\mathit{\_}\mathit{a}}^2{a}^2+2{\mathit{\_}\mathit{a}}^2-a^2+1}({\mathit{\_}\mathit{a}}^3-\mathit{\_}\mathit{a}{a}^2+\sqrt{{\mathit{\_}\mathit{a}}^2{a}^2-a^4+a^2}+\mathit{\_}\mathit{a})d\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1})x,y\left(x\right)=-\sqrt{a^2-1}x\}$$