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) |