Forms for Particular (Forced) Solutions [f_p(t)] for a Non-Homogeneous Differential Equation

df/dt + a f(t) = g(t)

if a=0, then f_p(t) = A ∫g(t)dt.

Form of the Excitation Function g(t)	Form of the Particular Solution fp(t)
K0	A
K0t	A+Bt
K0+K1t	A+Bt
K0+K1t+ K2t^2	A+Bt+ Ct^2
K0e^-bt (b=a)	Ae^-bt
K0e^-at	Ate^-at
K0Sin(wt)	ASin(wt) + BCos(wt)
K0Cos(wt)	ASin(wt) + BCos(wt)