2.1377   ODE No. 1377

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

$$y^{″}(x)=-\frac{b^{2}y(x)}{{(a^2+x^2)}^2}$$ ✓ Mathematica : cpu = 0.193292 (sec), leaf count = 163

$$\left\{\{y(x)\to \frac{i{c}_2\sqrt{a^2+x^2}{(1-\frac{ix}{a})}^{\sqrt{\frac{a^2+b^2}{a^2}}}{(1+\frac{ix}{a})}^{-\sqrt{\frac{a^2+b^2}{a^2}}}{e}^{i\sqrt{\frac{a^2+b^2}{a^2}}{\tan }^{-1}\left(\frac{x}{a}\right)}}{2a\sqrt{\frac{a^2+b^2}{a^2}}}+c_1\sqrt{a^2+x^2}{e}^{i\sqrt{\frac{b^2}{a^2}+1}{\tan }^{-1}\left(\frac{x}{a}\right)}\}\right\}$$ ✓ Maple : cpu = 0.252 (sec), leaf count = 83

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