This can be done in a number of ways; first, without additional packages, you can (locally) redefine \labelenumi:
\documentclass[a4paper]{report}
\usepackage{probsoln}
\loadallproblems{prob-easy}
\showanswers
\begin{document}
\begingroup
\renewcommand\labelenumi{\textbf{Question : Vraag \arabic{enumi}}}
\begin{enumerate}
\foreachproblem{\item\thisproblem}
\end{enumerate}
\endgroup
\end{document}
You can also achieve the desired result with the help of the enumitem package:
\documentclass[a4paper]{report}
\usepackage{probsoln}
\usepackage{enumitem}
\loadallproblems{prob-easy}
\showanswers
\begin{document}
\begin{enumerate}[label=\bfseries Question : Vraag \arabic*]
\foreachproblem{\item\thisproblem}
\end{enumerate}
\end{document}
Or, defining a dedicated list:
\documentclass[a4paper]{report}
\usepackage{probsoln}
\usepackage{enumitem}
\newlist{myproblems}{enumerate}{4}
\setlist[myproblems,1]{label=\bfseries Question : Vraag \arabic*}
\loadallproblems{prob-easy}
\showanswers
\begin{document}
\begin{myproblems}
\foreachproblem{\item\thisproblem}
\end{myproblems}
\end{document}

The file prob-easy.tex used in my example:
\begin{defproblem}{cosxsqsinx}%
\begin{onlyproblem}%
$y = \cos(x^2)\sin x$.%
\end{onlyproblem}%
\begin{onlysolution}%
\[\frac{dy}{dx} = -\sin(x^2)2x\sin x + \cos(x^2)\cos x\]
\end{onlysolution}%
\end{defproblem}
\begin{defproblem}{sinxsqsinx}%
\begin{onlyproblem}%
$y = \cos(x^2)\sin x$.%
\end{onlyproblem}%
\begin{onlysolution}%
\[\frac{dy}{dx} = -\sin(x^2)2x\sin x + \cos(x^2)\cos x\]
\end{onlysolution}%
\end{defproblem}
Update
In a comment it has been requested to have the title for each problem centered in a line of its own; here's one possibility:
\documentclass[a4paper]{report}
\usepackage{probsoln}
\newcounter{myprob}
\newenvironment{myproblems}
{\par\setcounter{myprob}{0}}
{\par}
\newcommand\MyProb{%
{\par\medskip\centering\refstepcounter{myprob}\bfseries Question : Vraag \arabic{myprob}\par\nobreak}%
}
\loadallproblems{prob-easy}
%\showanswers
\begin{document}
\begin{myproblems}
\foreachproblem{\MyProb\thisproblem}
\end{myproblems}
\end{document}

This was prob-easy.tex:
\begin{defproblem}{cosxsqsinx}%
\begin{onlyproblem}%
$y = \cos(x^2)\sin x$.%
\end{onlyproblem}%
\begin{onlysolution}%
\[\frac{dy}{dx} = -\sin(x^2)2x\sin x + \cos(x^2)\cos x\]
\end{onlysolution}%
\end{defproblem}
\begin{defproblem}{texttest}%
\begin{onlyproblem}%
Some text for the example. so the problem will have text and not necessarily a math expression.%
\end{onlyproblem}%
\begin{onlysolution}%
\[\frac{dy}{dx} = -\sin(x^2)2x\sin x + \cos(x^2)\cos x\]
\end{onlysolution}%
\end{defproblem}
\begin{defproblem}{sinxsqsinx}%
\begin{onlyproblem}%
$y = \cos(x^2)\sin x$.%
\end{onlyproblem}%
\begin{onlysolution}%
\[\frac{dy}{dx} = -\sin(x^2)2x\sin x + \cos(x^2)\cos x\]
\end{onlysolution}%
\end{defproblem}