2.1518   ODE No. 1518

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

$$x(x^2+1)y^{(3)}(x)+3(2x^2+1)y^{″}(x)-12y(x)=0$$ ✓ Mathematica : cpu = 0.245207 (sec), leaf count = 96

$$\left\{\{y(x)\to \frac{4c_1{x}^3+2c_2\sqrt{x^2+1}{x}^2+3c_3{x}^2+3c_3\sqrt{x^2+1}{x}^2\log (x)-3c_3\sqrt{x^2+1}{x}^2\log (\sqrt{x^2+1}+1)+2c_{1}x+c_3}{6x}\}\right\}$$

✓ Maple : cpu = 0.474 (sec), leaf count = 60

$$\{y\left(x\right)=\frac{1}{x}(3\mathit{A}\mathit{r}\mathit{t}\mathit{a}\mathit{n}\mathit{h}\left(\frac{1}{\sqrt{x^2+1}}\right)\sqrt{x^2+1}\mathit{\_}\mathit{C}\mathit{2}{x}^2+\mathit{\_}\mathit{C}\mathit{1}{x}^2\sqrt{x^2+1}+2\mathit{\_}\mathit{C}\mathit{3}{x}^3-3\mathit{\_}\mathit{C}\mathit{2}{x}^2+\mathit{\_}\mathit{C}\mathit{3}x-\mathit{\_}\mathit{C}\mathit{2})\}$$