A=30 0 -7029 3 -74140 -335(-~-~~-]) (-₁-²--E) (~--~-E])2, C₁= 3= 3, C₂= -5, C3 = 2=2has the following eigenpairs.Find the general solution to the following system of differential equations.y₁ = 30y₁ - 70y3Y₂ = 29y₁ + 3y2 – 74y3314y133y3y = k₁Ex: 6eEx: 6t + k₂t + k3t

The given system of differential equations,The aim is to find the solution to the system of…

Answered: A = 30 0 -70 29 3 -74 has the following…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Please do number 5
Match pairs of eigenvalues to the phase portraits of two dimensional systems. V=1,4 = 2 4₁=-1, 4-2 A₁ = -2+3i, A₂=-2-3i A₁ =21, A₂=-2i VA₁5, A₂=-3 A₁=1+√5, -1-i√5
Solve the system of differential equations{x'=29x−50yy'=15x−26y{x′=29x-50yy′=15x-26yx(0)=−13, y(0)=−8x(0)=-13, y(0)=-8The lesser of the two eigenvalues isIts corresponding eigevector is ⟨a,−3⟩⟨a,-3⟩. What is aa?a=a=The greater of the two eigenvalues isIts corresponding eigevector is ⟨2,b⟩⟨2,b⟩. What is bb?b=b=The solution to the system isx(t)x(t) = y(t)y(t) =
ÿ' = -[3. a. Find the eigenvalues and eigenvectors for the coefficient matrix. i 3/1-1/16 5 5 A₁ = i = 1 • Find the real-valued solution to the initial value problem yí = ly/₂ = Use t as the independent variable in your answers. 31(t) = 11 y2(t) = -15 15 2 -5 -3 3y1 + 2y2, -5y1 - 3y2, y. and A₂ = -i 9 y₁ (0) = 11, Y2(0) = −15. 9 V2 = T 1 i 3/4 + 1/4 5 35
1. (a) What are A, X and x' in matrix form x' = AX of the system of differential equations { FO (b) Find all eigenvalues and eigenvectors of A. (c) Find exponential solutions of the system of differential equations. (d) Verify your solutions. x₁ = 3x1 x2 = 5x1 + 2? x2
Q1 b. Please help me out with this question, please step by step Differential Equations
Solve the system of differential equations given in matrix form for the general solution. We must do this by calculating the eigenvalues and eigenvectors. Note: we get a repeated eigenvalue and must solve for the second eigenvector to get two linearly independent solutions for our general solution. Please explain how you calculate the second eigenvector
A system of ordinary differential equations has 2 x 2 state matrix with eigenvalues and corresponding eigenvectors (eigenpairs) A1 = 5, v1 = and A2 = -6, Based on the given eigenpairs write down the general solution to the associated system of differential equations. The solution must be written as a |¤1(t) single vector like a =
35. (a) Show that the eigenvalues of the 2 X 2 matrix a b A = c d] с а are the solutions of the quadratic equation 12 – tr(A)A + det A = 0, where tr(A) is the trace of A. (See page 162.) (b) Show that the eigenvalues of the matrix A in part (a) are A = {(a + d ± V(a – d)? + 4bc) (c) Show that the trace and determinant of the matrix A in part (a) are given by tr(A) - λι + λ and det A = λιλε where A, and A2 are the eigenvalues of A. 36. Consider again the matrix A in Exercise 35. Give conditions on a, b, c, and d such that A has (a) two distinct real eigenvalues, (b) one real eigenvalue, and (c) no real eigenvalues.
Xn Let vn be the solution to the discrete dynamical system: Yn 6xn – 13yn Oxn – 7yn Xn+1 Yn+1 [:] -3 If vo find vn- -1 Put the eigenvalues in ascending order when you enter xn, Yn below. Xn = Yn = )"+ )" ||
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 =

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