4.118   ODE No. 1118

$$\boxed{{\displaystyle x\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+((a+b)x+m+n)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+(abx+na+bm)y\left(x\right)=0}}$$

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

Mathematica: cpu = 0.093012 (sec), leaf count = 51 $$\left\{\{y(x)\to c_1{e}^{-ax}U(m,m+n,(a-b)x)+c_2{e}^{-ax}{L}_{-m}^{m+n-1}(x(a-b))\}\right\}$$

Maple: cpu = 0.063 (sec), leaf count = 43 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{-ax}\mathit{M}(m,m+n,x(a-b))+\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{-ax}\mathit{U}(m,m+n,x(a-b))\}$$