Question

For each nonhomogeneous linear equation below, determine what the guess solution yp would be for the method of undetermined coefficients.

with steps! Thank you

(a) y′′ − 4y′ + 13y = 80e−3t

(b) y′′−6y′+9y=(t+1)e3t

(c) y′′+4y=sin(2t)+t3−1

(d) 4y′′ − 4y′ + y = 16et/2

Answer 1

- 3+ Giren y". ug' +13y=doe o Auxiliary O r = 2 rt eq" in mr_unti3=0 4 Ibi =) . 2£3 Ye=e (acos (Btta Sin (3) 343) Jince é 3 -3t is not prenent in ye, form of of particular Sointion in - 3t Ae Cyp)

Given yl_by'tay=(tt) est Auxiliary ean in = Since Yp sur 68+9 - 0 =) (2-3)~=0 =) Y= 3,3 3 is a double root At+B) ( #e3ty ) = 7 E (a+P+6+) est E © (rea. form) y" +49 = sin(at) + t²_, Auriliary ear in prty -o =) metri Y c = a coscatta sin(at) vince Jin (2+) is prenent in yo t(A Cos (27) + B Sin (24) +(6+3+ot+ft+F) rea foom) Given 4Y"_4Y'ty_16th 487_ 4rt=0=) = € / / =) Y = (atat je Since ethet are prenent inte, A te the Yo d th 1 A.E. io H2 t2 yp ((rea form) =