Question

(1 point) Consider the Initial Value Problem 7-177] -[1] (a) Find the eigenvalues and eigenvectors for the coefficient matrix. Find the solution to the initial value problem. Give your solution in real form. Use the phase plotter pplanom in MATLAB to help you describe the trajectory An ellipse with clockwise orientation • 1. Describe the trajectory.

Answer 1

roy17 de 174 I-4 1-4X 1 I = (4x)² +120 7 -4-X x+y= 2 l x= -42 i Now (A - (-4+1) I) xp = 0 fusca) -24.0) (2) - 3] [%]- - [ 1 ] [8]: 8 x 77 + 2 = 0 Г X = | is that is eigen recton conmog ponding dit u te varit Au Tin head d = (-4-2) =div None Av Head an equals to & A - din Arad. So eigen rectan commos pending N2 Mone X+) - Glue thit & av e det - Ja & eit tage et] e-4 t Hone veit - rin 27 (lost tisine) sint te cost Cost te sint and delta I sint - é Cost ? Cost -i sint | None X (0) = (s] - Gui + Cl2 = { ecause so - Grela 3 iG-C2) = 5 - 3-6 i (3-262) = 5 3-26= -5e that is hora C221 (3+5 i). - (3-5i)

Gripit - a v e-it then arieit & V2 ell a Greit auelt - Reare it Nowe Regueit- se (3.5e) [Cart te sint] 3 tsint) + 5 Cost] 17 Cast & sint] T-3 sint h Cost7 13 Cost + 5 sint] So X (t) = (hvi e it & C2 V e-it] erut 2 e-at -3 sint tg Cost7 3 los ttg sint! Fon tea sectory: Here we have eigen values a -4ti, and if we look at xct) as to it goes to o. and due to presence of cost and sint it is Spiral. and the spiral is anti clock wise. and stable spiral