  Group theoretical methods are used to study some properties of the Riccati
equation, which is the only differential equation admitting a nonlinear
superposition principle. The Wei-Norman method is applied to obtain the
associated differential equation in the group $SL(2,R)$. The superposition
principle for first order differential equation systems and Lie-Scheffers
theorem are also analysed from this group theoretical perspective. Finally, the
theory is applied in the solution of second order differential equations like
time-independent Schroedinger equation
