How to change color in lstlisting (LaTeX) if the first symbol is $?

By formatting command-line snippets with LaTeX lstlisting, I want to separate input commands from their outputs as follows:

In the command-line snippet:

$date
Sat Jun  1 14:31:01 CEST 2019

$date has to be in blue

Sat Jun 1 14:31:01 CEST 2019 has to be in black

So the idea is to find all strings with the $ first symbol and colorize them.

I've search through usual commands as string or comment with rudimentary regexp but without luck. Is it really possible?

You could set up $ as comment character:

\documentclass{article}

\usepackage{listings}
\usepackage{xcolor}

\lstset{
commentstyle=\color{blue},
morecomment=[l]{$},
}

\begin{document}

\begin{lstlisting}
$date
Sat Jun  1 14:31:01 CEST 2019
\end{lstlisting}

\end{document}