2 2 X Questions 17 and 18 will deal with the linear system X' = - 2 3 pts Question 17 What are the eigenvalues to the linear system? Select the correct answer O 0,-4 O 2,2 O-2 2i 0,4 O 22i 4 pts Question 18 The solution of the linear system is Select the correct answer O None of the above (C X ce2 sin(2t) e cos(2t) 1 cos(2t) 0 sin(2t) 1 25 X c1e -2t sin(t) ce' cost...
(1 point) Solve the system 4 -2 dx II dt 10 -4 -3 with x(0) = -2 Give your solution in real form. Xı = -3cos(21)+(27sin(2t))/5 x2 = -2cos(2t)-11 sin(2t) An ellipse with counterclockwise orientation 1. Describe the trajectory.
Find a fundamental matrix for the system x'(t) = Ax(t) for the given matrix A. A 01 0 0 10 0 0 0 0 0 1 00 - 29 10 et 0 0 el 0 -t 0 et 0 0 et O A. X(t) = 1 0 OB. X(t) = 0 51(5 cos 2t - 2 sin 2t) e5t (5 sin 2t+2 cos 2t) 0 0 2t2 cos 5t - 5 sin 5t) 2 (2 sin 5t + 5 cos...
2. a. Show that y² + x – 3 = 0 is an implicit solution to dy/dx = -1/(2y) on the interval (-0, 3). b. Show that xy3 – xy: sin x = 1 is an implicit solution to dy_(x cos x + sin x - 1) y 3(x - x sin x) on the interval (0, /2).
QUESTION 3 After use Laplace Transform to transform the following initial value problem X" +x=e-t, x(0) = 1,x'(0) = 1, S-2 you should get X(s)= (write fraction as (S-2)/(5-4)(8+6) for -). Then, find (s-4)(8+6) x(t)= L-?{X(s)}= (write 5/6 by 5 -30 6' e^{-3t} by e and sin(2t) or cos(3t) by sin(2t) or cos(3t)).
NOTE: PLEASE DO Q.3 Part d and e
Answers are given below:
Question 3 (16 marks) Consider the periodic signal T v(t)24 cos(2t ) - 4 sin(5t - 2 The signal v is given as an input to a linear time-invariant continuous-time system with fre- quency response 4 0 lwl 2 2 jw H(w) lwlT 2, 1 2 jw (a) 3 marks] Find the fundamental period To and frequency wo of v (b) [3 marks] Express v in cosine sine...
Problem 4, Find, for 0-x-π, the arc-length of the segment of the curve R(t) = (2 cos t-cos 2t, 2 sin t-sin 2t) corresponding to 0< t < r
please show calculations
Solve the equation on the interval 0 s < 2t. 1) 2 cos 0+32 2) tan2 = 3 3) 2 sin2 = sino show calculation please 4) 2 cos2 - 3 cos 0+1=0 5) sin2 - Cos2 0 = 0 Simplify the expression 6) + tan e 1+ sin e cose 7) (1 + cot e)(1-cote) -sce Establish the identity. 8) (sin x)(tan x cos x - cotx cos x) = 1 - 2 cos2x 9) (1...
need help with #3
L. (3Upts) Consider the following ivp I)(24), 2(0) = 1.5. ut show that this ivp has a unique solution that exists everywhere on (-00, oo). Sk etch the graph of this solution with explanations (monotonicity, concavity,..) ow that the following initial value problem has a unique solution that exists for all t. cos(a) cos(et), a" +sin(a") cos(a') i r(0)-1, r"(0) = 0 . 4. (30 pts) Consider the following ivp r, y, 2x + y +...
At least one of the answers above is NOT correct. (1 point) Solve the system -6 -2 dc dt T 20 6 -3 with c(0) T: 1 Give your solution in real form. x1 = e^(t)-3cos (2t)- 10 sin(2t)) X2 = e^(1)(-33sin(2t)+cos(2t)) An ellipse with counterclockwise orientation 1. Describe the trajectory