Answer:
Yp = t[Asin(2t) + Acos(2t)]
Yp = t²[At² + Bt + C]
Step-by-step explanation:
The term "multiplicity" means when a given equation has a root at a given point is the multiplicity of that root.
(a) r1=-2i; r2=2i g(t)=2sin(2t) + 3cos(2t)
As you can notice the multiplicity of this equation is 1 since the roots r1 = 2i and r2 = 2i appear for only once.
The form of a particular solution will be
Yp = t[Asin(2t) + Acos(2t)]
where t is for multiplicity 1
(b) r1=r2=0; r3=1 g(t)= t² +2t + 3
As you can notice the multiplicity of this equation is 2 since the roots r1 = r2 = 0 appears 2 times.
The form of a particular solution will be
Yp = t²[At² + Bt + C]
where t² is for multiplicity 2
