4.192   ODE No. 1192

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

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

Mathematica: cpu = 10.168291 (sec), leaf count = 39 $$\left\{\{y(x)\to c_2{e}^{-x}{\int }_1^x{e}^{K[1]-\frac{1}{K[1]}}dK[1]+c_1{e}^{-x}\}\right\}$$

Maple: cpu = 0.109 (sec), leaf count = 53 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{-x}\mathit{H}\mathit{e}\mathit{u}\mathit{n}\mathit{D}(4,3,-8,5,\frac{x-1}{1+x})\sqrt{x}+\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{-x^{-1}}\mathit{H}\mathit{e}\mathit{u}\mathit{n}\mathit{D}(-4,3,-8,5,\frac{x-1}{1+x})\sqrt{x}\}$$