5.32   ODE No. 1480

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

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

Mathematica: cpu = 0.210027 (sec), leaf count = 93 $$\left\{\{y(x)\to \frac{c_3{e}^x{x}^{2v+2}\mathrm{\Gamma }(v+\frac{3}{2}){}_1{\tilde{F}}_1(v+\frac{3}{2};2v+3;-2x)}{\mathrm{\Gamma }(\frac{1}{2}-v)}+c_2{2}^{-2v-2}{e}^x{G}_{2,3}^{2,1}\left(2x|\begin{array}{c}1,v+\frac{3}{2}\\ 1,2(v+1),0\end{array}\right)+c_1{e}^x\}\right\}$$

Maple: cpu = 0.219 (sec), leaf count = 35 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^x+\mathit{\_}\mathit{C}\mathit{2}{x}^{v+1}{\mathit{I}}_{-v-1}\left(x\right)+\mathit{\_}\mathit{C}\mathit{3}{x}^{v+1}{\mathit{K}}_{v+1}\left(x\right)\}$$