2.1424   ODE No. 1424

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

$${\sin }^2(x)y^{″}(x)-y(x)(a{\sin }^2(x)+(n-1)n)=0$$ ✓ Mathematica : cpu = 0.187965 (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 = 2.179 (sec), leaf count = 120

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