5.51   ODE No. 1499

$$\boxed{{\displaystyle x^2\frac{{\mathrm{d}}^3}{\mathrm{d}{x}^3}y\left(x\right)-(x^2-2x)\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)-(x^2+{\nu }^2-1/4)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+(x^2-2x+{\nu }^2-1/4)y\left(x\right)=0}}$$

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

Mathematica: cpu = 0.232530 (sec), leaf count = 97 $$\left\{\{y(x)\to \frac{c_3{e}^x{x}^{\nu +\frac{1}{2}}\mathrm{\Gamma }(\nu +\frac{1}{2}){}_1{\tilde{F}}_1(\nu +\frac{1}{2};2\nu +1;-2x)}{\mathrm{\Gamma }(\frac{3}{2}-\nu )}+c_2{2}^{-\nu -\frac{1}{2}}{e}^x{G}_{2,3}^{2,1}\left(2x|\begin{array}{c}1,0\\ \frac{1}{2}-\nu ,\nu +\frac{1}{2},0\end{array}\right)+c_1{e}^x\}\right\}$$

Maple: cpu = 0.218 (sec), leaf count = 25 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^x+\mathit{\_}\mathit{C}\mathit{2}\sqrt{x}{\mathit{I}}_{\nu }\left(x\right)+\mathit{\_}\mathit{C}\mathit{3}\sqrt{x}{\mathit{K}}_{\nu }\left(x\right)\}$$