$$\DeclareMathOperator{\abs}{abs} \newcommand{\ensuremath}[1]{\mbox{#1}}$$
$\tag{\%{}o1}\label{o1} /usr/share/maxima/5.38.1/share/contrib/odes/odes.mac$
$\tag{eq}\label{eq}{{x}^{3}}-8{{x}^{2}}+x+9=0$
$\tag{\%{}o3}\label{o3} [x=\frac{2\sqrt{61}\,\cos{\left( \frac{\operatorname{atan}\left( \frac{9\sqrt{5003}}{709}\right) }{3}\right) }+8}{3},x=\frac{2\sqrt{61}\,\cos{\left( \frac{\operatorname{atan}\left( \frac{9\sqrt{5003}}{709}\right) -2\ensuremath{\pi} }{3}\right) }+8}{3},x=\frac{2\sqrt{61}\,\cos{\left( \frac{\operatorname{atan}\left( \frac{9\sqrt{5003}}{709}\right) +2\ensuremath{\pi} }{3}\right) }+8}{3}]$
$\tag{\%{}o4}\label{o4} [x=\left( -\frac{\sqrt{3}\%{}i}{2}-\frac{1}{2}\right) \,{{\left( \frac{\sqrt{5003}\%{}i}{6}+\frac{709}{54}\right) }^{\frac{1}{3}}}+\frac{61\left( \frac{\sqrt{3}\%{}i}{2}-\frac{1}{2}\right) }{9{{\left( \frac{\sqrt{5003}\%{}i}{6}+\frac{709}{54}\right) }^{\frac{1}{3}}}}+\frac{8}{3},x=\left( \frac{\sqrt{3}\%{}i}{2}-\frac{1}{2}\right) \,{{\left( \frac{\sqrt{5003}\%{}i}{6}+\frac{709}{54}\right) }^{\frac{1}{3}}}+\frac{61\left( -\frac{\sqrt{3}\%{}i}{2}-\frac{1}{2}\right) }{9{{\left( \frac{\sqrt{5003}\%{}i}{6}+\frac{709}{54}\right) }^{\frac{1}{3}}}}+\frac{8}{3},x={{\left( \frac{\sqrt{5003}\%{}i}{6}+\frac{709}{54}\right) }^{\frac{1}{3}}}+\frac{61}{9{{\left( \frac{\sqrt{5003}\%{}i}{6}+\frac{709}{54}\right) }^{\frac{1}{3}}}}+\frac{8}{3}]$