4.333   ODE No. 1333

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

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

Mathematica: cpu = 0.109014 (sec), leaf count = 70 $$\left\{\{y(x)\to c_1{i}^{-v}{x}^{-v/2}{}_2{F}_1(\frac{1}{2},-v;\frac{1}{2}-v;x)+c_2{i}^{v+1}{x}^{\frac{v+1}{2}}{}_2{F}_1(\frac{1}{2},v+1;v+\frac{3}{2};x)\}\right\}$$

Maple: cpu = 0.047 (sec), leaf count = 45 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{x}^{-\frac{v}{2}}{}_2\text{F}{}_1(\frac{1}{2},-v;\frac{1}{2}-v;x)+\mathit{\_}\mathit{C}\mathit{2}{x}^{\frac{1}{2}+\frac{v}{2}}{}_2\text{F}{}_1(\frac{1}{2},v+1;\frac{3}{2}+v;x)\}$$