5.70   ODE No. 1518

$$\boxed{{\displaystyle (x^2+1)x\frac{{\mathrm{d}}^3}{\mathrm{d}{x}^3}y\left(x\right)+3(2x^2+1)\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)-12y\left(x\right)=0}}$$

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

Mathematica: cpu = 0.241531 (sec), leaf count = 106 $$\left\{\{y(x)\to \frac{1}{3}{c}_1(2x^2+1)+\frac{1}{3}{c}_{2}x\sqrt{x^2+1}+\frac{c_3(2x^2+1)(3x^2+3\sqrt{x^2+1}{x}^2\log (x)-3\sqrt{x^2+1}{x}^2\log (\sqrt{x^2+1}+1)+1)}{6(2x^3+x)}\}\right\}$$

Maple: cpu = 0.374 (sec), leaf count = 56 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}x\sqrt{x^2+1}+\frac{\mathit{\_}\mathit{C}\mathit{2}}{x}(3x^2\sqrt{x^2+1}\mathit{A}\mathit{r}\mathit{t}\mathit{a}\mathit{n}\mathit{h}\left(\frac{1}{\sqrt{x^2+1}}\right)-3x^2-1)+\mathit{\_}\mathit{C}\mathit{3}(2x^2+1)\}$$