Consider the following system of first order differential equations:Y₁ = 3y₁+2y2-y3= 2y₁+6y2-2y3=-y₁-2y2+3y3.Solve the system using eigenvalues and eigenvectors.

Answered: Image /qna-images/answer/4fe11a47-edbc-480f-9b06-ff11c56dc324.jpg

Answered: Consider the following system of first…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter11: Differential Equations

Section11.CR: Chapter 11 Review

Problem 12CR

See similar textbooks

Similar questions

Write the system of differential equations given in the 1st photo in the normal form defined in the 2nd photo and solve the resulting system by means of the eigenvalues and eigen-vectors of the square matrix A.
Consider the system of differential equations -6y2, +6y1- a. Rewrite this system as a matrix equation y' = Ay. j' = • Compute the eigenvalues of the matrix A and enter them as a comma separated list.
Write the system of first-order linear differential equations represented by the matrix equation y′ = Ay. Then verify the general solution.
Write the homogeneous part of the differential equation system, namely f(x)= g(x)=0 in the normal form, obtained in the 1st photo, and solve the resulting system using eigen-values and eigen-vectors.
Consider the system of linear differential equations: y' = 1 2 a. Which of the following is the determinant equation that must be solved in order to find the eigenvalues? |1+A = 0 1 2+A |1–A 2 = 0 1 2 +A -1- A 2 = 0 1 2 - A |1–1 2 = 0 1 2 - A b. What are the eigenvalues? Write the eigenvalues as a pair of numbers, for instance: 5, 2. C. Which of the following is the general solution of the system of equations? y = cj le3t+ c2 -2 y = c1 + c2 e3t e-3t+ c2 y = ci y = c1 +c2 e-3t
Consider the linear system y' = a. Find the eigenvalues and eigenvectors for the coefficient matrix. A1 = , v1 = and A2 = v2 = For each eigenpair in the previous part, form a solution of y' = Aỹ. Use t as the independent variable in your answers. 1 and 2(t) = y1 (t) =
Consider the system of differential equations -24yı + 12y2, -30yı + 12y2. a. Rewrite this system as a matrix equation y' = Aj. j' = b. Compute the eigenvalues of the coefficient matrix A and enter them as a comma separated list. ||
using eigenvalues, find the general solution to the following system of equations. x' = x+ z y' = 3y z' = -y+z
Write the system of differential equations given in the question in the normal form defined as in the 3rd photo and solve the resulting system through the eigenvalues and eigen-vectors of the square matrix A.
S + 3y - 2r =0 (b) Express the as a first order system, and then find the eigen- values.
B4. Differential Equations: Complex-Vaued Eigenvalues Consider the linear system of linear equations. Determine the eigenvalues, associated eigenvectors and find the general solution. Then sketch the phase plane.
Consider the system of differential equations d.x = x + 4y dt dy 2x – y dt (i) Write the system (E) in a matrix form. (ii) Find a vector solution by eigenvalues/eigenvectors. (iii) Use the vector solution, write the solutions x(t) and y(t).

Recommended textbooks for you

Calculus For The Life Sciences

Calculus

ISBN:

9780321964038

Author:

GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:

Pearson Addison Wesley,

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Calculus For The Life Sciences

Calculus

ISBN:

9780321964038

Author:

GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:

Pearson Addison Wesley,

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

SEE MORE TEXTBOOKS

Consider the following system of first order differential equations: = 3y₁+2y2-y3 = 2y₁+62-203 Y'₁ =-y₁-2y₂+3y3. Solve the system using eigenvalues and eigenvectors.