2.1068   ODE No. 1068

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

$$v(v+1)y(x)+y^{″}(x)+\cot (x)y^{\prime }(x)=0$$ ✓ Mathematica : cpu = 0.149439 (sec), leaf count = 20

$$\left\{\{y(x)\to c_1{P}_v(\cos (x))+c_2{Q}_v(\cos (x))\}\right\}$$

✓ Maple : cpu = 0.929 (sec), leaf count = 45

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