Question

(1 point) Consider the systems of differential equations = 0.12 - 0.4y, = -0.4x + 0.7y. For this system, the smaller eigenvalue is !!! and the larger eigenvalue is Use the phase plotter pplane9.m in MATLAB to determine how the solution curves behave. A. The solution curves converge to different points. B. All of the solution curves converge towards 0. (Stable node) C. All of the solution curves run away from 0. (Unstable node) D. The solution curves race towards zero and then veer away towards infinity. (Saddle) (0) = 6, y(0) = 5 is The solution to the above differential equation with initial values <(t) = y(t) =

Answer 1

Giren - = 0.18-0.44 dx dt dy = de -0.42 + . - 0.1 -0.4 TE) (alt) YE) to find eigenvalue and eigenveton. [ 0 - 0/5 -215 7/10 det (A-AI)- to- -2 O = (x + 1) 1 - 1 + 78 - 4 10 These are smaller eigenvalues. eigen value is The - 10 and the largest elgen value is و To To fend eigen rector: ) For a- - TO eigen vector The is N = 12

PINO for dag 10 V. -12 The general so1n of system of eanis I act) = 72 dot co lylt) ( /2 option (1) The solution curves race towards Zero and then weer away towards gorioity. I saddle). @ Initial condr: x (o=6 1900) = C I2 C Y (o)=5 -12 6 5 = C12 C2 20- 2 C2 = 6 it C2 = 5 CI=12 C2 = 8 act) = 3 4 - g 4 e 10 9 + Yit) 14 e 1 + 8