Question

Use variation of parameters to solve the given nonhomogeneous system. = 4x - - 4y + 7 dx dt dy dt = 3x - 3y - 1 (x(t), y(t)) =

Answer 1

da dt =40-44 +7 dy olt >n-y-1 we can written as. '] = [1 -1] [%] + [3] Let A Now find eigenvalue and eigencector of A. A-110 -4 CO (4-2)(-3-2) +1220 →? - -12 +1220 »-coa (2-1)= 20,1 2 eigenvalues 2,20, dzel for, doo A-(OI- [:] (*)R, [5 -1} ****, [:) - [ ] [*]-[] ... 2- yo- eigenvector corresponding eigenvalue a, 20 is [1]

nel A-101 [3 -13 BR, ( =*] ****82, [ ] -1.361.13 Ş920 h 4 / 5 []=[*) *[1] & eigenvector corresponding eigensualue tq = 1 [3] 13] tq et [1] + V2 et []=[]Le :) (*) [pt 3 = [_] (][:]-[x]" -> 4 -21-4 - [m] :13 -66:12 25

:=-25 * Vi= 5-25 dt V, = -256 V₂ = 24 et * V2 = /29 € * dt & Vq = -296t [?]=6258) °[$]+(+218) [Behing -32 aast + -29 - 25t -2st 32 -25t-24 ( 3 [order] = e.[1]+ee*[3] + [20-34] - 1 * е et Aca -25t-32 a + Caet -25t-24