4.191   ODE No. 1191

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

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

Mathematica: cpu = 0.008501 (sec), leaf count = 110 $$\left\{\{y(x)\to \frac{2c_2{e}^{\frac{1}{2}(\log (x)-x)}(i\sinh \left(\frac{x}{2}\right)-\frac{2i\cosh \left(\frac{x}{2}\right)}{x})}{\sqrt{\pi }\sqrt{-ix}}+\frac{2c_1{e}^{\frac{1}{2}(\log (x)-x)}(\frac{2\sinh \left(\frac{x}{2}\right)}{x}-\cosh \left(\frac{x}{2}\right))}{\sqrt{\pi }\sqrt{-ix}}\}\right\}$$

Maple: cpu = 0.016 (sec), leaf count = 25 $$\{y\left(x\right)=\frac{\mathit{\_}\mathit{C}\mathit{1}(x-2)}{x}+\frac{\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{-x}(x+2)}{x}\}$$