4.235   ODE No. 1235

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

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

Mathematica: cpu = 0.026503 (sec), leaf count = 50 $$\left\{\{y(x)\to c_2\sin (\sqrt{a}\log (\sqrt{x^2-1}+x))+c_1\cos (\sqrt{a}\log (\sqrt{x^2-1}+x))\}\right\}$$

Maple: cpu = 0.015 (sec), leaf count = 43 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{(x+\sqrt{x^2-1})}^{i\sqrt{a}}+\mathit{\_}\mathit{C}\mathit{2}{\left({(x+\sqrt{x^2-1})}^{i\sqrt{a}}\right)}^{-1}\}$$