Question

9.7.5 Question Help Use the method of undetermined coefficients to find a general solution to the system x'(t) = Ax(t) + f(t), where A and f(t) are given. 3 e 2t 0 -1 0 A= -1 0 0 ,f(t) = 3 sin 3t 0 0 1 t X(t) = 0

DIFFERENTIAL EQUATIONS / Linear Algebra

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Answer 1

x(t) AX(4)十f(t) ㅇ | 0 2라 ge + | -1 이 f) ) A 0 3 Sin3t t 의 da ता 이 0 3e24 0 O 니. 0 dy ता + 33734 ) o 0 d2 + ता 0 ( da dt J +3025 du dt -243Sin3t 2 w de dt - Ztt. 대 on both side we get coperat FO Link C dy It + d42 belt 2 - - x264] + set 원 A tel N - 2t 6e- 3Sn3t- A.E m용 스 mail cof qtteeet 1 97g =anbittng Corstenty

at Lot 3p = A e + B.Sin3t + Claszt Dup to Bears 34 Be Sint - 2ne2t Boup = 4A e = YA e 27 +(-9B) Sin3t - qc Canist cue 4 ne²t from ® get 2t -qB sinat -90 Canst - Al-Bainst -Clanst = 6e2t 3 sin 3t Equating co-efficients we get 3A = 6 A=a. -IOB=-3 B = 3/10 toc ao h cao up a.de PO Sin at ett 1. X= Get tezét + 2e??? + 20° + Sch3t. y = - da dt + 3 e²t = -[cret-cset tye?t ta Casat »367+2e =-gettegét-et- of Canst 2t

from 3 =Ztt dz de dz dt . ex -t dt t Constant ster zat: Infiftit A (2et) =tet -Jo + di = -tet-etta dizanbitary Z=-t-1 teti zet = e toleo . Constant 0 Hemee the general general sal" is. at as gett eget the +20 3 sinat ga -get teget re eet Causat T 2 = det - -(tt) + 9, 62 , 41 = anitary constants.