4.297   ODE No. 1297

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

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

Mathematica: cpu = 0.033504 (sec), leaf count = 52 $$\left\{\{y(x)\to c_2\sin \left(\frac{\sqrt{b}{\sinh }^{-1}\left(\sqrt{a}x\right)}{\sqrt{a}}\right)+c_1\cos \left(\frac{\sqrt{b}{\sinh }^{-1}\left(\sqrt{a}x\right)}{\sqrt{a}}\right)\}\right\}$$

Maple: cpu = 0.016 (sec), leaf count = 61 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{(\sqrt{a}x+\sqrt{a{x}^2+1})}^{i\sqrt{b}\frac{1}{\sqrt{a}}}+\mathit{\_}\mathit{C}\mathit{2}{\left({(\sqrt{a}x+\sqrt{a{x}^2+1})}^{i\sqrt{b}\frac{1}{\sqrt{a}}}\right)}^{-1}\}$$