Is it possible create an oval and colored boxed using fancybox?

Question

I would like my red box to be oval. Here is my code :

\documentclass[12pt,a4paper]{article}

\usepackage[latin1]{inputenc} 
\usepackage[T1]{fontenc}      
\usepackage[french]{babel}
\usepackage{amsmath,amssymb}
\usepackage{psfrag}
\usepackage{fancybox}
\usepackage{pgfplots}

\begin{document}

$$\ddot{x}+\colorbox{red!10}{$\frac{\omega_0}{Q}$}\dot{x}+\omega_0^2 x=0$$

\end{document}

Answer 1

Similar to Bernard's answer, with \tcboxmath from tcolorbox.

\documentclass[12pt,a4paper, french]{article}

\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{babel}
\usepackage{amsmath,amssymb}
\usepackage[table]{xcolor}
\usepackage[most]{tcolorbox}

\tcbset{%
  highlightstyle/.style={enhanced,colback=red!40,boxsep=0pt,frame hidden}
}


\begin{document}

\[ \ddot{x}+\tcboxmath[highlightstyle,sharp corners]{\frac{\omega_0}{Q}}\dot{x}+\omega_0^2 x=0 \]

\[ \ddot{x}+\tcboxmath[highlightstyle,auto outer arc, arc=15pt]{\frac{\omega_0}{Q}}\dot{x}+\omega_0^2 x=0 \]

\[ \ddot{x}+\tcboxmath[highlightstyle,octogon arc,arc is angular]{\frac{\omega_0}{Q}}\dot{x}+\omega_0^2 x=0 \]

\end{document} 

Answer 2

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}