Question

Use X X + X, = e^*c + eAt e-AS F(s) ds to find the general solution of the given system. = Jto 1 X' = 0 4 e8t X(t) =

Answer 1

Given thal x'e ( Xt eak 7eLet A- The chanactenstie equalionA 1-A こ0 4コ expamecon tho datermunant gers )4-A)O にl amd Aこ4 → the eigen ralues A The egenuedts X b is n CA-1I)XO ( 44 3 0 3x20 20 Simce kto amanir X10, Let k1. Thon Xiに Us an eigemved

The osgemvectd b A 4 sgaem by CA A2) X2-0 ( 1-4 4-4 ( 0 From the fenst get3x10 E ontntronal now we Since x2キ0, Let k (C) ()+(e) Thon Xc= C e C e The mattux X LS et Xニ The imNense K ズー Adj x [py det X ef 46 1 et e4t

Χ uioυ 3- / Ο Πls /tot 4t e? j25α -f[. dt TI δira. dt e4t rett dt Τ Ε Juwaufpfαδν ωμ eυ Cυ2 4Ε e Γ. εεγε (6 ) '2) t e 46 dt et-)e εt

The gemeral seution s 4t -t-1 X C e