You are solving a 2x2 system of the form : PỸ + where P has constant entries with real different eigenvalues. s(t) = Decide which of the following statements is correct: I can find a particular solution using the undetermined coefficients method with a try function of the form Y(t) = sin(t)ā + cos I can find a particular solution using the undetermined coefficients method with a try function of the form Y(t) = (cos(t) + sin(t))ä I can only find the general solution for this problems using the Variation of Parameters method. Undetermined Coefficients won't work in this case. I can find the general solution using the undetermined coefficients method. To find the particular solution I should use a with a try function of the form Y(t) = sin(t)ā

You are solving a 2x2 system of the form : PỸ + where P has constant entries with real different eigenvalues. s(t) = Decide which of the following statements is correct: I can find a particular solution using the undetermined coefficients method with a try function of the form Y(t) = sin(t)ā + cos I can find a particular solution using the undetermined coefficients method with a try function of the form Y(t) = (cos(t) + sin(t))ä I can only find the general solution for this problems using the Variation of Parameters method. Undetermined Coefficients won't work in this case. I can find the general solution using the undetermined coefficients method. To find the particular solution I should use a with a try function of the form Y(t) = sin(t)ā

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

Related questions

Q: Consider the following system. dx dt dy dt Find the eigenvalues of the coefficient matrix A(t).…

Q: Consider the initial value problem y, j(0) = a. Find the eigenvalue A, an eigenvector v1, and a…

Q: Q96 THE LINEAR SYSTEM IS -6 -4 x² = [ {²+] = × 12 8 THE EIGENVECTORS AND EIGENVALUES ARE: A₂ = 2 √ ₂…

A: NOTE: Refresh your page if you can't see any equations..The given matrix is,The given eigenvalues…

Q: Find the minimum and maximum values of Q(x) under the constraint ||x||=1 and find the eigenvectors…

Q: b. ‹- ( _ 1 ) *. The coefficient matrix has only one eigenvalue, λ = 5, which has algebraic…

A: The following steps are used to find the solution of a system of first order linear homogeneous…

Q: Apply the eigenvalue method to find the general solution of the given system. Find also th…

Q: Let x(t) = x₁ (t) x'₂ (t) = If x (0) [ x₂(t): = x₁(t) x₂ (t) be a solution to the system of…

Q: Rewrite the following systems of differential equations as first order systems, written in the…

Q: Use the eigenvalue-eigenvector method to solve the initial value problem 2 -7 0 X = 5 10 4 -21 Х,…

Q: 1. Using the eigenvalue method, solve the initial value problem. Leave your solution in real-valued…

A: Step 1:Step 2:

Q: Give a solution to the system 6 2 -25 8 æ(0) by solving the IVP with initial condition - 8 30 # (t)…

Q: Suppose that f(t) = e (1−2i)t is a complex solution for an unknown second-order linear equation…

Q: In the following problem apply the eigenvalue method to find a general solution of the given system.…

A: Given: The system of equations are x'1=3x1+4x2 x'2=3x1+2x2 ; x1(0)=x2(0)=1 To find: The general…

Q: In the following problem apply the eigenvalue method to find a general solution of the given system.…

A: We have to find the particular solution of the given system of differential equations. First we have…

Q: Given below is the second-order system of differential equations: d2x/dt2 = -x - 3y, d2y/dt2 = -3x…

A: Given: Second-order system of differential equations: d2xdt2=-x-3y, d2ydt2=-3x-y…

Q: Consider the initial value problem , j(0) = a. Find the eigenvalue A, an eigenvector v1, and a…

Q: Solve this.

A: Consider the following spring mass system.

Q: Sive a solution to the system 2 y' - 25 - 8 æ(0)] -8 y solving the IVP with initial condition 30 -8…

Q: 2. For the system of equations: dx = a11x + a12y, dt dy a21x + az2y. dt First, review lecture notes…

Question

You are solving a 2x2 system of the form:

\[ \vec{Y}' = P \vec{Y} + \begin{bmatrix} 0 \\ \cos(t) \end{bmatrix} \]

where $ P $ has constant entries with real different eigenvalues.

Decide which of the following statements is correct:

1. (Option): I can find a particular solution using the undetermined coefficients method with a try function of the form

\[ \vec{Y}(t) = \sin(t)\vec{a} + \cos(t)\vec{b} \]

2. (Option): I can find a particular solution using the undetermined coefficients method with a try function of the form

\[ \vec{Y}(t) = (\cos(t) + \sin(t))\vec{a} \]

3. (Option): I can only find the general solution for this problem using the Variation of Parameters method. Undetermined Coefficients won't work in this case.

4. (Option): I can find the general solution using the undetermined coefficients method. To find the particular solution I should use a try function of the form

\[ \vec{Y}(t) = \sin(t)\vec{a} \]

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Matrix Eigenvalues and Eigenvectors$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

Please show step-by-step solution and do not skip steps. Explain your entire process in great detail. Explain how you reached the answer you did.
(2 cos 2t / 19. Assume that a real 2 x 2 matrix A has an eigenvalue of A1 = 3+ 2i with a corresponding eigenvector = (6) Find the general solution of the system of differential equations 2i given by 글 %=D Az. cos 2t sin 2t 교(t) = cie3t ( sin 2t + cze³t 2 cos 2t cos 2t sin 2t a(t) = c1e3t + cze3t -2 sin 2t 2 cos 2t (. cos 2t sin 2t a(t) Ciešt + cze3t sin 2t - cos 2t ( -2 cos 2t sin 2t a(t) = cie3t + cze3t sin 2t -2 cos 2t cos 2t ( 2 sin 2t ) sin 2t a(t) = c1e3t + cze³t 2 cos 2t
This is the first part of a two-part problem. Let P=[-: 1 5₁(t) = [(41) 5₂(t) = - sin(4t). a. Show that y₁ (t) is a solution to the system ÿ' = Pÿ by evaluating derivatives and the matrix product y(t) = = 0 [1] -4 Enter your answers in terms of the variable t. -4 sin(4t) -4 cos(4t)] ÿ₁ (t) [181-18] b. Show that y₂ (t) is a solution to the system ÿ' = Pÿ by evaluating derivatives and the matrix product Enter your answers in terms of the variable t. 04] 32(t) = [-28]|2(t) 181-181
I already know the eigenvalues are -2+6i, and 2-6i, and the eigenvector is [6i,1] , and [-6i,1], im just struggling finding the overall solution
Solve the following initial value problems for the systems of equations using the matrix method. Find eigenvalues and eigenvectors by hand (but you can use technology to check your answers) (a) (b) x' = y' I x2 - 6x + 3y -4x-y 2 2x1 - 5x2 4x1 - 2x2 x(0) = 3, y(0) = -2. 2₁ (0) = 1, ₂ (0) = 1. 7
5. Apply the eigenvalue method to find the general solution of the given system. Fina diso ahe corresponding particular solution by using the initial values. (x = 9x1 + 5x2 x½ = -6x1 – 2x2 Initial: x, (0) = 1,x2(0) = 0
Everything we've done with systems of 2 linear, constant co- efficient, homogeneous differential equations works for larger systems as well. Ask wolframalpha.com for the eigenvalues and eigenvectors of the following system of three differential equations, and use the result to write the general solution: -2 -4 2 *m-Biss X' (t) -2 1 2 X(t) 4 2 5 =