Question

3x-2y = 7 and 4x+3y = -2 in second equation

Answer 1

Answer:

Sketch phase portraits for the following linear systems: (a) c = 0, y = x + 2y; (b) ¿ = x + 2y, j = 0; (c) c = 3x + 4y, j = 4x – 3y; (d) ¿ = 3x + y, y = -x + 3y; (e) c = y, y = -x – 2y; (f) ở = - g, g = 9 – . A very simple mechanical oscillator can be modeled using the second- order differential equation dax dx + 7 + 25x = 0, dt2 dt where x measures displacement from equilibrium. (a) Rewrite this equation as a linear first order system by setting i = y. (b) Sketch phase portraits when (i) y = -8, (ii) u = 0, (iii) u = 8, and (iii) u = 26. (c) Describe the dynamical behavior in each case given that x(0) = 1 and c(0) = 0.