Question

Use variation of parameters to solve the given nonhomogeneous system. X' = ( X + -1 9 9t e X(t) = Need Help? Read It Watch It Talk to a Tutor

Answer 1

Given x'=(osa Y't Gia Da + Cent] comparing with x'=Ax+g (4) qui= (-) where A= (48) The chamcteristic equation of ARS 12_(ard)dt lad-bc) zo -> 1m91 + (0+8)=0 =) A²09148=0 solving weget d=1,8 consider Harmogeneous system (tad (22) = (3) put i=1 =) (8**)-(3) R2 R2_, -178 16,0)=133 ni+8H2=0 = 2,=84 SM For dia, to ) - ( en Dam (SJ weget eigen vector v = (8) Pued=83) (* 1916') = 13) >(*%)02-18 R₂ - 8R2_R, -8117892=0 = 1,=4 Q)-(*)--)) For y=8, we get eigen vector 2 X(t) = q elitvi taget (1) X(11= 9 (9]+66+ (1) consider 0041 - Set eft .

. ēt -ēt 8 c so to - ( ) .. on ge) = + ( Jed + (131 Lee :Juttoguid= ) - 인가 set_elot 드 de +8일가 누 -8Et 일아 육일가 pd) = npctgy set ( et e8 -8Ek 4t et 유인가 64 t용 8년 + 1 용 84임에 *] ( 하이 ( = () +/ -8 휴 누 -61 + 28 85 -7 LE To 하 Hence General solution is X(t)=X&ti+ Xp (4) xuthe a et (CJ +4 2t[] + Crist) -