4.423   ODE No. 1423

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

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

Mathematica: cpu = 0.072009 (sec), leaf count = 70 $$\left\{\{y(x)\to c_1\sqrt[4]{{\cos }^2(x)-1}{P}_{-\frac{1}{2}}^{\frac{1}{2}\sqrt{1-4a}}(\cos (x))+c_2\sqrt[4]{{\cos }^2(x)-1}{Q}_{-\frac{1}{2}}^{\frac{1}{2}\sqrt{1-4a}}(\cos (x))\}\right\}$$

Maple: cpu = 0.203 (sec), leaf count = 165 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}\sqrt[4]{2\cos \left(2x\right)+2}{}_2\text{F}{}_1(\frac{1}{4}\sqrt{1-4a}+\frac{1}{4},\frac{1}{4}\sqrt{1-4a}+\frac{1}{4};\frac{1}{2};\frac{\cos \left(2x\right)}{2}+\frac{1}{2})\sqrt{-2\cos \left(2x\right)+2}{(\frac{\cos \left(2x\right)}{2}-\frac{1}{2})}^{\frac{1}{4}\sqrt{1-4a}}\frac{1}{\sqrt{\sin \left(2x\right)}}+\mathit{\_}\mathit{C}\mathit{2}{(2\cos \left(2x\right)+2)}^{\frac{3}{4}}{}_2\text{F}{}_1(\frac{1}{4}\sqrt{1-4a}+\frac{3}{4},\frac{1}{4}\sqrt{1-4a}+\frac{3}{4};\frac{3}{2};\frac{\cos \left(2x\right)}{2}+\frac{1}{2})\sqrt{-2\cos \left(2x\right)+2}{(\frac{\cos \left(2x\right)}{2}-\frac{1}{2})}^{\frac{1}{4}\sqrt{1-4a}}\frac{1}{\sqrt{\sin \left(2x\right)}}\}$$