4.365   ODE No. 1365

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

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

Mathematica: cpu = 0.093512 (sec), leaf count = 72 $$\left\{\{y(x)\to c_1\sqrt{x^2+1}{e}^{i\sqrt{a+1}{\tan }^{-1}(x)}+\frac{i{c}_2\sqrt{x^2+1}{e}^{-i\sqrt{a+1}{\tan }^{-1}(x)}}{2\sqrt{a+1}}\}\right\}$$

Maple: cpu = 0.031 (sec), leaf count = 65 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}\sqrt{x^2+1}{\left(\frac{x+i}{-x+i}\right)}^{\frac{1}{2}\sqrt{a+1}}+\mathit{\_}\mathit{C}\mathit{2}\sqrt{x^2+1}{\left(\frac{x+i}{-x+i}\right)}^{-\frac{1}{2}\sqrt{a+1}}\}$$