2.1420   ODE No. 1420

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

$${\cos }^2(x)y^{″}(x)-y(x)(a{\cos }^2(x)+(n-1)n)=0$$ ✓ Mathematica : cpu = 0.434688 (sec), leaf count = 134

$$\left\{\{y(x)\to c_1{i}^{1-n}{\cos }^{1-n}(x){}_2{F}_1(-\frac{n}{2}-\frac{i\sqrt{a}}{2}+\frac{1}{2},-\frac{n}{2}+\frac{i\sqrt{a}}{2}+\frac{1}{2};\frac{3}{2}-n;{\cos }^2(x))+c_2{i}^n{\cos }^n(x){}_2{F}_1(\frac{n}{2}-\frac{i\sqrt{a}}{2},\frac{n}{2}+\frac{i\sqrt{a}}{2};n+\frac{1}{2};{\cos }^2(x))\}\right\}$$

✓ Maple : cpu = 0.307 (sec), leaf count = 123

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