2.1333   ODE No. 1333

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

$$y^{″}(x)=\frac{v(v+1)y(x)}{4x^2}-\frac{(3x-1)y^{\prime }(x)}{2(x-1)x}$$ ✓ Mathematica : cpu = 0.108049 (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 = 0.075 (sec), leaf count = 45

$$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{x}^{-\frac{v}{2}}{}_2\text{F}{}_1(\frac{1}{2},-v;\frac{1}{2}-v;x)+\mathit{\_}\mathit{C}\mathit{2}{x}^{\frac{v}{2}+\frac{1}{2}}{}_2\text{F}{}_1(\frac{1}{2},v+1;\frac{3}{2}+v;x)\}$$