Auto width tcolorbox around equation

Question

I am using tcolorbox to draw boxes around equations. Since the box widths are equal to the equation widths, long titles are often shrunk, hence looking ugly, as shown here:

Is there any way to draw a box of auto-width around the equation and title?

A minimal working example is here:

\documentclass[11pt]{article}
\usepackage[many]{tcolorbox}

\begin{document}
\begin{equation}
\tcbhighmath[title=A long title hence does not fit]{\lambda=at^2}
\end{equation}

\begin{equation}
\tcbhighmath[title=short-title]{\lambda=at^2+bt^3}
\end{equation}
\end{document}

Answer 1

A different approach by defining a new key autowidth title that lets the minimum text width to be equal to the the title length

\documentclass[11pt]{article}
\usepackage[many]{tcolorbox}

\pgfkeysdef{/tcb/autowidth title}{
    \pgfmathwidth{"#1"}
    \def\width{\pgfmathresult pt} % \width = title length
 %
    \tcbset{title=#1,
            tcbox width=minimum center,
            text width=\width % minimum text width = title length
           }
 }

\begin{document}
\begin{equation}
\tcbhighmath[autowidth title=A long title hence does not fit ]{\lambda=at^2}
\end{equation}

\begin{equation}
\tcbhighmath[autowidth title=short-title]{\lambda=at^2+bt^3}
\end{equation}

\end{document}

Answer 2

From this excellent macro of Thomas F. Sturm: ....fit the width...., here there is my adapt answer:

\documentclass[11pt]{article}
\usepackage[many]{tcolorbox}
\tcbset{longtitle/.style={%
  title={#1},
  before upper={\begin{tabular}{@{}l@{}l}\phantom{#1}\\[\the\dimexpr-\ht\strutbox-\dp\strutbox]},
  after upper={\end{tabular}}}
  }

\begin{document}
\begin{equation}
\tcbhighmath[longtitle=A long title hence does now fit]{$\lambda=at^2$}%<---- for a double dollar
\end{equation}


\begin{equation}
\tcbhighmath[title=short-title]{\lambda=at^2+bt^3}%<---- without a double dollar
\end{equation}
\end{document}

A fix for avoiding the $ characters in the main argument:

\documentclass[11pt]{article}
\usepackage{array}
\usepackage[many]{tcolorbox}

\tcbset{longtitle/.style={%
  title={#1},
  before upper={%
    $\begin{array}{@{}>{\displaystyle}l@{}}
    \mbox{\phantom{#1}}\\[\the\dimexpr-\ht\strutbox-\dp\strutbox]%
  },
  after upper={\end{array}$}},
}

\begin{document}

\begin{equation}
\tcbhighmath[longtitle=A long title hence does now fit]{\lambda=at^2}
\end{equation}

\begin{equation}
\tcbhighmath[title=short-title]{\lambda=at^2+bt^3}                              
\end{equation}

\end{document}