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

 

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

 

if a=0, then fp(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+ K2t2

A+Bt+ Ct2

K0e-bt (b=a)

Ae-bt

K0e-at

Ate-at

K0Sin(wt)

ASin(wt) + BCos(wt)

K0Cos(wt)

ASin(wt) + BCos(wt)