Suppose that the differential equation x' = Ax is such that A is a 2 × 2 matrix with (1) eigenvalues A1 = 5 and A2 = 3 and corresponding eigenvectors vị = and v2 = the solution that satisfies the initial condition x(0) : Explain what happens to the trajectory of this solution as t → 0. Circle one of the items below. i. becomes parallel to the vector vị = (-). ii. becomes parallel to the vector v2 = iii. tends towards the point (0,0). iv. Spirals away from the origin v. none of the above

Suppose that the differential equation x' = Ax is such that A is a 2 × 2 matrix with (1) eigenvalues A1 = 5 and A2 = 3 and corresponding eigenvectors vị = and v2 = the solution that satisfies the initial condition x(0) : Explain what happens to the trajectory of this solution as t → 0. Circle one of the items below. i. becomes parallel to the vector vị = (-). ii. becomes parallel to the vector v2 = iii. tends towards the point (0,0). iv. Spirals away from the origin v. none of the above

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

3. Classify the given partial differential equation as hyperbolic, parabolic, or elliptic. a. а2u azu J2u дх2 дхду дуг + + = 0 b. д2u a2u az = at2 ?х2
1
VII. Run two iterations using normalized power iteration method for the following matrix and initial vector. Roughly predict the dominate eigenvalue and corresponding eigenvector. A = [ ²₁ 2] ₁ x₁ = 1 []
Consider the system of differential equations For this system, the smaller eigenvalue is (-39/10) [Note-- you may want to view a phase plane plot (right click to open in a new window).] If y'= Ay is a differential equation, how would the solution curves behave? • All of the solutions curves would converge towards 0. (Stable node) All of the solution curves would run away from 0. (Unstable node) and the larger eigenvalue is The solution curves would race towards zero and then veer away towards infinity. (Saddle) The solution curves converge to different points. The solution to the above differential equation with initial values (0) = 4, y(0) = 3 is (t)= (49/12)*e^((-9/10)*t)-(1/12)*e^((-19/10)*t) y(t) = (49/12)*e^((-9/10)*t)+(5/12)*e^((-19/10)*t) da dt dy dt = -1.4x +0.75y, = 1.66667 3.4y. (-9/10)
The behaviour of an unforced mechanical system is governed by the differential equation 5 2 -1 0 x(1) = 3 6-9 x(t), x(0) = 1 1 1 1 0 (a) Show that the eigenvalues of the system matrix are 6, 3, 3 and that there is only one linearly independent eigenvector corresponding to the eigenvalue 3. Obtain the eigenvectors corresponding to the eigenvalues 6 and 3 and a further generalized eigenvector for the eigenvalue 3. (b) Write down a generalized modal matrix M and confirm that AM = MJ for an appropriate Jordan matrix J. x(t) = Me M-¹x(0) obtain the solution to the given differential equation. (c) Using the result
Read each of the two statements carefully. Choose A(if both statements are true) , B(if the 1st statement is true but the 2nd is false), c(if the 1st statement is false and the 2nd is true and D(if both statements are false. 1st: dx2 =0 is a 2nd order linear partial differential equation ду? + 2nd : dx? =0 is a 1st degree partial differential equation ду2 A) D В) в A D) c
The following Partial differential equation: a2u a?u a?u -2 ax2 -6" + Su = 0 is classified as ду "дхду "ду? + O A. Parabolic О В. Нурerbolic O C. Elliptic O D. None of the above Reset Selection
12- The system x = x + 4y, y' = y + x has two eigenvectors....
Do only 4th part U may need part 3rd I have uploaded half part of 3rd
Show your work
Suppose that a 2 x 2 matrix A with real entries has an eigenvalue X = 1 + 3i with corresponding 4 i [12] eigenvector 1 + 2i Which of the following is NOT a solution of the linear system y' = Ay? y(t) = et y(t) = et y(t) = et y(t) = et 4 cos(3t) sin(3t) [cos(3t) + 2 sin(3t). 4 cos(3t) + sin(3t) cos(3t) 2 sin (3t) - cos(3t) + 4 sin(3t) 2 cos(3t) + sin(3t) cos (3t) - 4 sin (3t) -2 cos(3t) - sin(3t)
Transform the given system of differential equations into an equivalent system of first-order differential equations. x' - 3x' - 5x+2y=0 y'' +6y' - 6x-3y = sin t Let x₁ = x, X₂ = X', Y₁ = y, and y₂ = y'. Complete the system below. X₁' X₂ X Y2 II 11 11 11