A new method is described to study dynamical systems characterized by linear ordinary differential equations. The method is aimed at studying the time-varying properties of the resulting solution of the differential equation. In contrast to the standard methods where one solves the differential equation and then uses a time-frequency distribution, for example the Wigner distribution, to ascertain the time-frequency properties of the solution we show that one can obtain a differential equation for the Wigner distribution of the solution. We discuss a number of advantages for doing so.