2.1386   ODE No. 1386

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

$$y^{″}(x)=\frac{18y(x)}{(2x+1{)}^2(x^2+x+1)}$$ ✓ Mathematica : cpu = 0.0911558 (sec), leaf count = 108

$$\left\{\{y(x)\to \frac{c_1(x^2+x+1)}{(2x+1{)}^2}+\frac{c_2(16x^3+24x^2-12\sqrt{3}{x}^2{\tan }^{-1}\left(\frac{2x+1}{\sqrt{3}}\right)+30x-12\sqrt{3}x{\tan }^{-1}\left(\frac{2x+1}{\sqrt{3}}\right)-12\sqrt{3}{\tan }^{-1}\left(\frac{2x+1}{\sqrt{3}}\right)+11)}{(2x+1{)}^2}\}\right\}$$

✓ Maple : cpu = 0.073 (sec), leaf count = 68

$$\{y\left(x\right)=\frac{\mathit{\_}\mathit{C}\mathit{1}(x^2+x+1)}{{(2x+1)}^2}+\frac{\mathit{\_}\mathit{C}\mathit{2}}{{(2x+1)}^2}((36x^2+36x+36)\arctan \left(\frac{(2x+1)\sqrt{3}}{3}\right)-16\sqrt{3}(x^3+x^2+\frac{11x}{8}+3/16))\}$$