4.197   ODE No. 1197

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

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

Mathematica: cpu = 0.018002 (sec), leaf count = 78 $$\left\{\{y(x)\to c_1{e}^{\frac{1}{2}(x-\log (x))}{J}_{\frac{1}{2}\sqrt{4a+1}}(-\frac{ix}{2})+c_2{e}^{\frac{1}{2}(x-\log (x))}{Y}_{\frac{1}{2}\sqrt{4a+1}}(-\frac{ix}{2})\}\right\}$$

Maple: cpu = 0.032 (sec), leaf count = 49 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{\frac{x}{2}}{\mathit{I}}_{\frac{1}{2}\sqrt{4a+1}}\left(\frac{x}{2}\right)\frac{1}{\sqrt{x}}+\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{\frac{x}{2}}{\mathit{K}}_{\frac{1}{2}\sqrt{4a+1}}\left(\frac{x}{2}\right)\frac{1}{\sqrt{x}}\}$$