4.290   ODE No. 1290

$$\boxed{{\displaystyle (27x^2+4)\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+27x\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)-3y\left(x\right)=0}}$$

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

Mathematica: cpu = 0.175022 (sec), leaf count = 103 $$\left\{\{y(x)\to c_1\cosh \left(\frac{\sqrt{-27x^2-4}{\tan }^{-1}\left(\frac{3x}{\sqrt{-9x^2-\frac{4}{3}}}\right)}{3\sqrt{27x^2+4}}\right)+i{c}_2\sinh \left(\frac{\sqrt{-27x^2-4}{\tan }^{-1}\left(\frac{3x}{\sqrt{-9x^2-\frac{4}{3}}}\right)}{3\sqrt{27x^2+4}}\right)\}\right\}$$

Maple: cpu = 0.015 (sec), leaf count = 47 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}\sin \left(\frac{1}{3}\arctan \left(3\frac{\sqrt{3}x}{\sqrt{-27x^2-4}}\right)\right)+\mathit{\_}\mathit{C}\mathit{2}\cos \left(\frac{1}{3}\arctan \left(3\frac{\sqrt{3}x}{\sqrt{-27x^2-4}}\right)\right)\}$$