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2. Given the system of differential equations i = Ar, where A = 2 ) (1)...
(1 point) Find the most general real-valued solution to the linear system of differential equations LT-18 210 [x'][17 –20||2| I g] [ 15 -18l| = C + C2 help (formulas) help (matrices) y(t) In the phase plane, this system is best described as a source / unstable node sink / stable node saddle center point / ellipses spiral source spiral sink Onone of these
Q5. (15pt] Consider the following system of differential equations. it t = = Ctyt - 1, c + gì - 2. (a) (3pt) Find the equilibria of this system. (b) (5pt] Draw the phase diagram of the system and analyze the stability of the equilibria. (c) (7pt] Linearize the system around (1,1) by using Taylor approximation. Find the general so- lution of this linear system of differential equations and analyze the stability of the equilibria.
Find the most general real-valued solution to the linear system of differential equations (1 point) a. Find the most general real-valued solution to the linear system of differential -5 -36 x. -5 equations x 1 CHH x1 (t) = C1 x2 (t) b. In the phase plane, this system is best described as a O source/ unstable node Osink /stable node Osaddle center point ellipses Ospiral source spiral sink none of these tsi O O O (1 point) a. Find...
a. Find the most general real-valued solution to the linear system of differential equations a' 2 -9 -2 2. 21(t) 음을 + C2 22(t) b. In the phase plane, this system is best described as a O source / unstable node sink / stable node saddle center point / ellipses spiral source spiral sink none of these preview ang
This is a differential equations problem 2. Given the system of differential equations 0.2 0.005ry, --0.5y+0.01ry, which models the rates of changes of two interacting species populations, describe the type of z- and y-populations involved (exponential or logistic) and the nature of their interaction (competition, cooperation, or predation). Then find and characterize the system's critical points (type and stability). Determine what nonzero r- and y-populations can coexist. Ther construct a phase plane portrait that enables you to describe the long...
(1 point) a. Find the most general real-valued solution to the linear system of differential equations a' 2.(0) z(t) C + c b. In the phase plane, this system is best described as a O source / unstable node sink/stable node O saddle O center point/ ellipses spiral source Ospiral sink
8. Consider the nonhomogeneous linear system of differential equations 1 1 1 -1 u = -1 11 1 1 u-et 1 1 2 3 First of all, find a fundamental matrix and the inverse matrix of the fundamental matrix of the corresponding homogeneous linear system. Then given a particular solution 71 uy(t) = et 1 2 find the general solution of the nonhomogeneous linear system of differential equations. Hint: det(A - \I) = -(1 – 2)?(1+1)
(1 point) a. Find the most general real-valued solution to the linear system of differential equations ã' = 21(t) = C1 + c 22(t) b. In the phase plane, this system is best described as a source / unstable node sink / stable node Osaddle O center point / ellipses spiral source Ospiral sink O none of these
16-ol a. Find the most general real-valued solution to the linear system of differential equations i 4 -8 21(t) C1 + C2 12(t) b. In the phase plane, this system is best described as a O source / unstable node O sink/stable node O saddle O center point / ellipses spiral source spiral sink none of these
Consider the linear system given by the following differential equation y(4) + 3y(3) + 2y + 3y + 2y = ů – u where u = r(t) is the input and y is the output. Do not use MATLAB! a) Find the transfer function of the system (assume zero initial conditions)? b) Is this system stable? Show your work to justify your claim. Note: y(4) is the fourth derivative of y. Hint: Use the Routh-Hurwitz stability criterion! c) Write the...