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 = 0.272014 (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 = 0.372 (sec), leaf count = 60

$$\{y\left(x\right)=\frac{3c_2\sqrt{x^2+1}{x}^2\mathrm{arctanh}\left(\frac{1}{\sqrt{x^2+1}}\right)+2c_3{x}^3+c_1\sqrt{x^2+1}{x}^2-3c_2{x}^2+c_{3}x-c_2}{x}\}$$