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 = 0.23799 (sec), leaf count = 109

$$\left\{\{y(x)\to c_1\sqrt{a^2+x^2}{e}^{i\sqrt{\frac{b^2}{a^2}+1}{\tan }^{-1}\left(\frac{x}{a}\right)}+\frac{i{c}_2\sqrt{a^2+x^2}{e}^{-i\sqrt{\frac{a^2+b^2}{a^2}}{\tan }^{-1}\left(\frac{x}{a}\right)}}{2a\sqrt{\frac{a^2+b^2}{a^2}}}\}\right\}$$

✓ Maple : cpu = 0.552 (sec), leaf count = 91

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