2.1436   ODE No. 1436

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

$$y^{″}(x)=-\frac{1}{4}y(x){\csc }^2(x)(-4n^2+4v(v+1){\sin }^2(x)-{\cos }^2(x)+2)$$ ✓ Mathematica : cpu = 0.543398 (sec), leaf count = 42

$$\left\{\{y(x)\to c_1\sqrt[4]{{\cos }^2(x)-1}{P}_v^n(\cos (x))+c_2\sqrt[4]{{\cos }^2(x)-1}{Q}_v^n(\cos (x))\}\right\}$$

✓ Maple : cpu = 0.27 (sec), leaf count = 140

$$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}\sqrt[4]{2\cos \left(2x\right)+2}{}_2\text{F}{}_1(-\frac{v}{2}+\frac{n}{2},\frac{1}{2}+\frac{v}{2}+\frac{n}{2};\frac{1}{2};\frac{\cos \left(2x\right)}{2}+\frac{1}{2})\sqrt{-2\cos \left(2x\right)+2}{(\frac{\cos \left(2x\right)}{2}-\frac{1}{2})}^{\frac{n}{2}}\frac{1}{\sqrt{\sin \left(2x\right)}}+\mathit{\_}\mathit{C}\mathit{2}{(2\cos \left(2x\right)+2)}^{\frac{3}{4}}{}_2\text{F}{}_1(1+\frac{v}{2}+\frac{n}{2},\frac{1}{2}-\frac{v}{2}+\frac{n}{2};\frac{3}{2};\frac{\cos \left(2x\right)}{2}+\frac{1}{2})\sqrt{-2\cos \left(2x\right)+2}{(\frac{\cos \left(2x\right)}{2}-\frac{1}{2})}^{\frac{n}{2}}\frac{1}{\sqrt{\sin \left(2x\right)}}\}$$