Question

21. In each of these problems, determine a suitable form for Y (t) if the method of undetermined coefficients is to be used. Do not evaluate the constants.

a. y"" - 2y" + y' = t³ + 2e^t
b. y''' - y' = te^-t + 2cost
c. y^4 - 2y'' + y = e^t + sin(t)
d. y^4 + 4y" = sin 2t + te^t + 4
e. y^4 - y''' - y" + y' = t² + 4 + tsin(t)
f. y^4 + 2y''' + 2y" = 3e^t + 2te^-t + e^-t sin(t)​

Answer 1

a. Y(t) = At³ + Be^t + Ct² + Dt + E

b. Y(t) = At + B + Ce^t + Dsin(t) + Ecos(t)

c. Y(t) = Aet + Bte^t + Csin(t) + Dcos(t)

d. Y(t) = At³ + Bt² + Ct + D + Ecos(2t) + Fsin(2t)

e. Y(t) = At² + Bt + C + Dsin(t) + Ecos(t) + Fsin(t) + Gcos(t)

f. Y(t) = Aet + Bte^-t + Ccos(t) + Dsin(t) + E + Ft + G