Here we have a system of differential equations. (dx/dt) = 11x + 8y, (dy/dt) = 8x - y. The coefficient matrix, [11 8] [8 -1] has eigenvectors: [1] and [2] [-2] [1] With corresponding eigenvalues of -5 and 15. what is the general solution of this system?

Here we have a system of differential equations. (dx/dt) = 11x + 8y, (dy/dt) = 8x - y. The coefficient matrix, [11 8] [8 -1] has eigenvectors: [1] and [2] [-2] [1] With corresponding eigenvalues of -5 and 15. what is the general solution of this system?

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: Express the given system of higher-order differential equations as a matrix system in normal form.…

A: We will convert the given system to a system of first order differential equations in matrix form.

Q: (c) x': ·(3 = 2₂). x, x(0) = [1,0]T 9 5 -6 -2

Q: The matrix -1 2 3-6 has a eigenvalues -7,0 with eigenvec- tors (-1,3) and (2, 1). Write the general…

A: For a given differential equation where eigen values and respective eigen vectors are given. We have…

Q: Let A be an m x n matrix, and let B and C have sizes for which the indicated sums and products are…

A: If the product AB is defined, the entry in row i and column j of AB is the sum of the products of…

Q: Suppose Un+1= A U₁ is a matrix difference equation which describes discreet population changes from…

A: Given: The equation of difference matrix is Un+1=AUn. To find: (a) The general solution of the…

Q: Let y' = Ay be a system of differential equations where A = The matrix has spectrum X(A) = {2} and c…

Q: Use the eigenvalue and Method to find the general eigen vector solution of the following finst onden…

Q: The zeros in the given matrix make its characteristic polynomial easy to calculate. Find the general…

Q: a. Find the eigenvalues and eigenvectors of the matrix (8) A₁ = 21(t) x₂(t) v1 = b. Solve the system…

Q: Consider the system of differential equations à = Ax where A is a real-valued 2x2 matrix. Suppose…

A: We can solve it by principle of superposition.

Q: Given the system C. dx dt dx, f. dt = 4x₁ - 1x₂ a. Write the above system in matrix form ie dx dt b.…

Q: 2. x' = Find the general solution of the system of equations. -20 28 8 -14 22 4 X -21 21 14

A: Find: the general solution of the system of equations. x'=-20288-14224-212114x

Q: Consider the following system of coupled second-order equations, x + 4x1 = x2 x+ 4x2 = 0. Re-write…

A: please see the next step for solution

Q: Solve the given (matrix) linear system: 3cos(t) X' = ; x+ (3cos() [2 14 - 2 2et

A: Given X'=2-142X+3cos(t)2et The objective is to solve the above system.

Q: A = 30 0 -70 29 3 -74 has the following eigenpairs. 14 0 -33 r₁ = 2, C₁ 5 = -ED) (₁-₁₁-E) (---₁--E)…

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

Q: A system of coupled ODEs, where x = x(t), are expressed in the matrix form = 7 x' = (-1034)x where x…

A: note : Since you have posted question with multiple sub parts, we will provide the solution only to…

Q: Consider the following system. Find the eigenvalues of the coefficient matrix A(t). (Enter your…

A: Given- Consider the following system. X' = 8-88-12X To find- Find the eigenvalues of the…

Q: You may use a calculator to perform basic calculations on these problems: (just label when using…

A: Given, x'=-103020-30-1x

Q: Identify the matrix equation that corresponds to the system of first order differential equations…

Q: Solve using the method of undetermined coefficients: y" + 3y" – 10y' = 2 + xe* %3D

A: Given: y''' + 3y'' - 10y' = 2 + xex

Q: A system of differential equations can be created for two masses connected by springs between one…

Q: Finding

Q: 39 2-31]2, 2004] 니 dz de where 2 =/ 2₁1 and 12 = [ 2.1 2-√² ] Z

Q: a. Find the eigenvalues and corresponding eigenvectors for the matrix P = A₁ = -2 x₁(t)= x₂ (1) =…

Q: 2. (a) Let A be a square matrix of order tv 11 with the corresponding and V = Find exponential…

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: 2 2 -6 8. The general solution of x' = x is: (Hint: 6 is an eigenvalue.) 2 -1 -3 -2 - 1 -2 3 1 (a) x…

Q: Consider the initial value problem (a) Find the eigenvalues and eigenvectors for the coefficient…

Q: Given the system of equations, - [] 1 5 x' х, х(0) -3 = use the fact that the eigenpairs of the…

Q: Express the given system of higher-order differential equations as a matrix system in normal form.…

A: Given system of equations: x''+3x+6y=0y''-5x=0 Aim: Reduce this ODE to first order system of…

Question

Here we have a system of differential equations.

(dx/dt) = 11x + 8y, (dy/dt) = 8x - y.

The coefficient matrix,

[11 8]
[8 -1]

has eigenvectors:

[1] and [2]

[-2] [1]

With corresponding eigenvalues of -5 and 15.

what is the general solution of this system?

With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.

Expert Solution

This question has been solved!

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

SEE SOLUTION Check out a sample Q&A here

Step 1: Introduction

VIEW

Step 2: Solution

VIEW

Solution

VIEW

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

(b) Determine the eigenvalues and eigenvectors of the matrix Hence, write down the associated modal matrix P and diagonal spectrum matrix D, and use these to solve the following system of differential equations * = 4x-2y j =x+y
Consider the Initial Value Problem: x₁ x2 X₁ = 0,₁ % v1 = 2x1 + 2x2 = = -4x12x₂² x1 (0) = 4 x2 (0) 6 (a) Find the eigenvalues and eigenvectors for the coefficient matrix. 181 = , and X₂ = ₁0₂ = (b) Solve the initial value problem. Give your solution in real form. x1 x2 = An ellipse with clockwise orientation phase plotter pplane9.m in MATLAB to describe the trajectory. [B] 1. Use the
Q1 b. Please help me out with this question, please step by step Differential Equations
Express the given system of higher-order differential equations as a matrix system in normal form. x" + 5x+6y=0 y" - 5x=0 Which of the following sets of definitions allows the given system to be written as an equivalent system in normal form using only the new variables? O A. x₁ = x¹, x₂ =y' O B. X₁ =X, X₂=X', X3 = Y, X4=y' OC. x₁ = x, X₂=x", X3 = Y. X4=y" OD. x₁ = x¹, x₂ = x¹, x₂ =y', X4=y" Write the system of equations using matrix notation. Select the correct choice below and fill in the answer box to complete your choice. (Type an exact answer.) O A. O B. X₁ X₂ x₁² X1 x2 x3 X4 X1
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 =
Express the given system of higher-order differential equations as a matrix system in normal form. x" + 6x + 7y=0 y" - 2x=0 Which of the following sets of definitions allows the given system to be written as an equivalent system in normal form using only the new variables? OA. X₁ = x¹, x₂ = y' O B. X₁ =X, X2₂=X'', X3 = Y, X4 =y" O c. x₁ = x¹, x₂ = x¹, X3 = y', X4 =y" O D. x₁ = x, X₂ = x', X3 = Y, X4 = y' Write the system of equations using matrix notation. Select the correct choice below and fill in the answer box to complete your choice. (Type an exact answer.) OA. B. X₁ X₂ X₁ S w X4 || X₁ X2 x1 3 ... W X4 ро
Let A be a 2 x 2 matrix with eigenvalues X₁ = -3 and >₂ = -1 and [1] an H Let x(t) be the position of a particle at time t. Suppose we solved the initial corresponding eigenvectors V₁ = value problem x = Ax, x(0) = [3] -ce + c₂e-t x(t) = = [2(t)] = [ qe * +ge + -3t Search and C2= -3t and V2 = to obtain then C1=
Q3. (a) If Ax = 2 x, determine the eigenvalues and the corresponding eigenvectors for A= G ) 2 3. Hence, write down the associated modal matrix P and diagonal matrix D, and use these values to solve the following system differential equations: *1 = X1 + 4 x2 X2 = 2 x1 + 3 x2 Given that when t = 0, x1 = 0 and x2 = 2. (b) Use the 4th order Runge Kutta method to solve the differential equation: dy e* y dx for values of x 0 (0.2) 0.4 given that y 1 when x 0. %3D Give your answers correct to 5 decimal places. Obtain the analytical solution of the differential equation and compare the analytical solution when x = 0.4 with the values obtained using Runge Kutta,
find the general solution of x‘= ax,exponentials of matrices must be explicitly calculated if used in your answer.