4.275   ODE No. 1275

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

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

Mathematica: cpu = 0.037005 (sec), leaf count = 120 $$\left\{\{y(x)\to c_1{e}^{\frac{1}{2}(\sqrt{m^2-1}\log (x)-x)}U(\frac{1}{2}(-2l+m+\sqrt{m^2-1}),\sqrt{m^2-1}+1,x)+c_2{e}^{\frac{1}{2}(\sqrt{m^2-1}\log (x)-x)}{L}_{\frac{1}{2}(2l-\sqrt{m^2-1}-m)}^{\sqrt{m^2-1}}(x)\}\right\}$$

Maple: cpu = 0.110 (sec), leaf count = 55 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathit{M}}_{l-\frac{m}{2}+\frac{1}{2},\frac{1}{2}\sqrt{m-1}\sqrt{m+1}}\left(x\right)\frac{1}{\sqrt{x}}+\mathit{\_}\mathit{C}\mathit{2}{\mathit{W}}_{l-\frac{m}{2}+\frac{1}{2},\frac{1}{2}\sqrt{m-1}\sqrt{m+1}}\left(x\right)\frac{1}{\sqrt{x}}\}$$