2.1518   ODE No. 1518

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

$$3(2x^2+1)y^{″}(x)+x(x^2+1)y^{(3)}(x)-12y(x)=0$$ ✓ Mathematica : cpu = 0.229018 (sec), leaf count = 104

$$\left\{\{y(x)\to \frac{1}{3}{c}_1(2x^2+1)+\frac{1}{3}{c}_{2}x\sqrt{x^2+1}-\frac{c_3(2x^2+1)(3(x^4+x^2){\tanh }^{-1}\left(\sqrt{x^2+1}\right)-\sqrt{x^2+1}(3x^2+1))}{6\sqrt{x^2+1}(2x^3+x)}\}\right\}$$ ✓ Maple : cpu = 0.343 (sec), leaf count = 60

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