Based on the provided information about the characteristic roots and the right hand side function g(t), determine the appropriate form of a particular solution to be used with the undetermined coefficient method.

(a) r1=-2i; r2=2i g(t)=2sin(2t) + 3cos(2t)
(b) r1=r2=0; r3=1 g(t)= t^2 +2t + 3

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

1. PV = nRT. and solving for n (moles F2) we have

n = PV/RT = (1.50 atm)(15.0 L)/(0.0821 Latm/Kmol)(280K)

n = 0.9788 moles F2

mass NaCl = 0.9788 mol F2 x 2 mol NaCl x 58.4 g/mol = answer

Explanation:To find mass NaCl at STP just substitute 1 atm for pressure and 273K for temperature in the above equation and follow the rest of the calculations above.