4.116   ODE No. 1116

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

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

Mathematica: cpu = 0.053507 (sec), leaf count = 43 $$\left\{\{y(x)\to c_1{e}^{-ax}U(b,b+n,ax)+c_2{e}^{-ax}{L}_{-b}^{b+n-1}(ax)\}\right\}$$

Maple: cpu = 0.078 (sec), leaf count = 35 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{-ax}\mathit{M}(b,b+n,ax)+\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{-ax}\mathit{U}(b,b+n,ax)\}$$