4.421   ODE No. 1421

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

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

Mathematica: cpu = 0.248031 (sec), leaf count = 67 $$\left\{\{y(x)\to c_1{e}^{-\sqrt{-a^2}x}{\cos }^{n-1}(ax)+\frac{c_2{e}^{\sqrt{-a^2}x}{\cos }^{n-1}(ax)}{2\sqrt{-a^2}}\}\right\}$$

Maple: cpu = 0.063 (sec), leaf count = 27 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{(\cos \left(ax\right))}^n+\mathit{\_}\mathit{C}\mathit{2}{(\cos \left(ax\right))}^{n-1}\sin \left(ax\right)\}$$