2.1365   ODE No. 1365

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

$$y^{″}(x)=-\frac{ay(x)}{{(x^2+1)}^2}$$ ✓ Mathematica : cpu = 0.0773902 (sec), leaf count = 104

$$\left\{\{y(x)\to \frac{i{c}_2\sqrt{x^2+1}(1-ix{)}^{\sqrt{a+1}}(1+ix{)}^{-\sqrt{a+1}}{e}^{i\sqrt{a+1}{\tan }^{-1}(x)}}{2\sqrt{a+1}}+c_1\sqrt{x^2+1}{e}^{i\sqrt{a+1}{\tan }^{-1}(x)}\}\right\}$$ ✓ Maple : cpu = 0.137 (sec), leaf count = 59

$$\{y\left(x\right)=\sqrt{x^2+1}({\left(\frac{x+i}{-x+i}\right)}^{-\frac{1}{2}\sqrt{a+1}}\mathit{\_}\mathit{C}\mathit{2}+{\left(\frac{x+i}{-x+i}\right)}^{\frac{1}{2}\sqrt{a+1}}\mathit{\_}\mathit{C}\mathit{1})\}$$