4.424   ODE No. 1424

$$\boxed{{\displaystyle {(\sin \left(x\right))}^2\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)-(a{(\sin \left(x\right))}^2+n(n-1))y\left(x\right)=0}}$$

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

Mathematica: cpu = 0.171022 (sec), leaf count = 90 $$\left\{\{y(x)\to c_1\sqrt[4]{{\cos }^2(x)-1}{P}_{\frac{1}{2}i(2\sqrt{a}+i)}^{\frac{1}{2}(2n-1)}(\cos (x))+c_2\sqrt[4]{{\cos }^2(x)-1}{Q}_{\frac{1}{2}i(2\sqrt{a}+i)}^{\frac{1}{2}(2n-1)}(\cos (x))\}\right\}$$

Maple: cpu = 0.203 (sec), leaf count = 125 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{(\frac{\cos \left(2x\right)}{2}-\frac{1}{2})}^{\frac{n}{2}}{}_2\text{F}{}_1(\frac{n}{2}+\frac{i}{2}\sqrt{a},\frac{n}{2}-\frac{i}{2}\sqrt{a};\frac{1}{2};\frac{\cos \left(2x\right)}{2}+\frac{1}{2})+\mathit{\_}\mathit{C}\mathit{2}{(2\cos \left(2x\right)+2)}^{\frac{3}{4}}{}_2\text{F}{}_1(\frac{1}{2}+\frac{i}{2}\sqrt{a}+\frac{n}{2},\frac{1}{2}-\frac{i}{2}\sqrt{a}+\frac{n}{2};\frac{3}{2};\frac{\cos \left(2x\right)}{2}+\frac{1}{2}){(\frac{\cos \left(2x\right)}{2}-\frac{1}{2})}^{\frac{n}{2}}\sqrt[4]{-2\cos \left(2x\right)+2}\frac{1}{\sqrt{\sin \left(2x\right)}}\}$$