ABSTRACT
I y' + ay = F(t) (7.5) where a is a real constant, which can be positive or negative.
The exact solution of Eq. (7.5) is the sum of the complementary solution yc(t) and the particular solution yp(t):
yet) = yc(t) + ypCt) The complementary solution ycCt) is the solution of the homogeneous ODE:
y~ + aYe = 0
(7.6)
(7.7) The complementary solution, which depends only on the homogeneous ODE, describes the inherent properties of the ODE and the response of the ODE in the absence of external stimuli. The particular solution ypCt) is the function which satisfies the nonhomogeneous term F(t):
(7.8) The particular solution describes the response of the ODE to external stimuli specified by the nonhomogeneous term F(t).
