$$\DeclareMathOperator{\abs}{abs} \newcommand{\ensuremath}[1]{\mbox{#1}}$$
$\tag{\%{}o1}\label{o1} /usr/share/maxima/5.38.1/share/contrib/odes/odes.mac$
$\tag{eq}\label{eq}{{x}^{3}}-3x-1=0$
$\tag{\%{}o3}\label{o3} [x=2\cos{\left( \frac{\ensuremath{\pi} }{9}\right) },x=2\cos{\left( \frac{5\ensuremath{\pi} }{9}\right) },x=2\cos{\left( \frac{7\ensuremath{\pi} }{9}\right) }]$
$\tag{\%{}o4}\label{o4} [x=\left( -\frac{\sqrt{3}\%{}i}{2}-\frac{1}{2}\right) \,{{\left( \frac{\sqrt{3}\%{}i}{2}+\frac{1}{2}\right) }^{\frac{1}{3}}}+\frac{\frac{\sqrt{3}\%{}i}{2}-\frac{1}{2}}{{{\left( \frac{\sqrt{3}\%{}i}{2}+\frac{1}{2}\right) }^{\frac{1}{3}}}},x=\left( \frac{\sqrt{3}\%{}i}{2}-\frac{1}{2}\right) \,{{\left( \frac{\sqrt{3}\%{}i}{2}+\frac{1}{2}\right) }^{\frac{1}{3}}}+\frac{-\frac{\sqrt{3}\%{}i}{2}-\frac{1}{2}}{{{\left( \frac{\sqrt{3}\%{}i}{2}+\frac{1}{2}\right) }^{\frac{1}{3}}}},x={{\left( \frac{\sqrt{3}\%{}i}{2}+\frac{1}{2}\right) }^{\frac{1}{3}}}+\frac{1}{{{\left( \frac{\sqrt{3}\%{}i}{2}+\frac{1}{2}\right) }^{\frac{1}{3}}}}]$