Here are two ways with pstricks
.
Comments aside: the language option should be loaded with the document class, since babel 3.9
, to ensure language-dependent packages be aware of the document main language. Also, you shouldn't use the $$ ... $$
construction, which is plain TeX, always prefer \[ ... \]
.
\documentclass[12pt,a4paper, french]{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{babel}
\usepackage{amsmath,amssymb}
\usepackage[table]{xcolor}
\usepackage{psfrag}
\usepackage{fancybox}
\usepackage{pst-node}
\usepackage{auto-pst-pdf} %% to compile with pdflatex -shell-escape under TeX Live or MacTeX, pdflatex --enable-write18 under MiKTeX
\usepackage{pgfplots}
\begin{document}
\[ \ddot{x}+\colorbox{red!10}{$\dfrac{\omega_0}{Q}$}\dot{x}+\omega_0^2 x=0 \]
\[ \ddot{x}+\raisebox{\dimexpr-0.5\height +0.25ex}{\psovalbox*[fillcolor = red!20]{$ \dfrac{\omega_0}{Q} $}}\dot{x}+\omega_0^2 x=0 \]
\[ \ddot{x}+\raisebox{\dimexpr-0.5\height +0.25ex}{\psframebox*[fillcolor = red!30, framearc =.6]{$ \dfrac{\omega_0}{Q} $}}\dot{x}+\omega_0^2 x=0 \]
\end{document}

tcolorbox
?\tcbhighlight
isn't really time - consuming. By the way,$$...$$
is deprecated for more than 20 years.\tcbhighmath