1 A Pair of Linear Differential Equations

( ) ( ) ( ) 2 22 21 f t y a t x a t y + + = & (1) where x(t) and y(t) are two dynamic variables, aij are given constants and i f are constant forcing functions and they may take the form of a once-and-for-all exogenous shift from one constant level to the other. The solution to the above system will be two functions x(t) and y(t) that satisfy (1) and will consist of the general solution related to the homogeneous part of the system plus a particular solution related to the nonhomogeneous part. The homogeneous system corresponding to (1) is y a x a x 12 11 + = &