Question

(13) x1 = 4x1 - x2 + 3e2t x1(0) = - x2 = 2x1 + x2 + 2t X2(0) = 42

Differential Equations Question

Method of Elimination - Initial Value Problems.

Find the solution of the following IVPs.

Answer 1

Sol à = 42, - ng+ 3 e at ng= an, eng & ait and x = usi, -ig + beant * = 42-(022, ++4 ) +6edct * = 45,- (an, #3, +44, +3e28 +21) & beat n = 52,- 62, + 3 eart-Ict 2 - 5*;+691 = 3ed4-2f A, E = m2-5m + 6 = 0 m = 3,2 e = e, egut + co eart xp = 7 3 editat - 3 it eart - 12 [ 1 - 0 + 60 Jt - - 24 edit - ( it to mp = -3.4224- ] then x, (t) = c eset + eart - 3 t eart its

and porro na = -; +421 + 300 € = -3c, eget – ao cart + 3e act+ axa de act + t uc, eget tuc eget - 12 et eget hogy -20 +3 eact 18. ng=c, eact to edit a bit eact +Beact -ut - $6 . § 18 m and 18 so X, (0) = -5 Xalo)=47 9 from) and (2) a + - = -5 C, + C +94 = 47 [c, = -ca , + C2 = 0 c, +22=0 So solution is xi (t) = c est ac, eact-3 it eat - I - - ceart -c, eat - Get eart to eact