Answered: Reduce the fourth order DE 2y) +7y"…

Reduce the fourth order DE 2y) +7y" -9y' =-e' with I.Cs y(0) = y'(0) = 4, y"(0) = y"(0) = -3, to the system %3D in the matrix form.

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: 10.Solve the given (matrix) linear system: 1 21 [1 X' 13 %3D

Q: Consider the linear system a. Find the eigenvalues and eigenvectors for the coefficient matrix.…

Q: Q.I Suppose a simple economy with only an agriculture industry and a steel industry with the…

A: Let the gross production for agriculture and steel industry be respectively x and y. Then it can be…

Q: 1. Given the function h(x) = (3x-6)/(2x -4) find h^-1(x)

A: Since you have posted a multiple question according to guildlines I will solve first(1)question for…

Q: Help please

Q: dz (b) Determine the by using the Chain rule with the following information: ds z = cos (rªy^) – sin…

Q: x – 5y – z = 1 y – z = 2 x – 5z =1 1. Write the system above in Ax=b form using matrices and find…

Q: Consider the linear system Find the eigenvalues and eigenvectors for the coefficient matrix. A₁ = 15…

A: For given system, the coefficient matrix is To find eigenvalues of ,…

Q: You have this system which is nonhomogeneous 니 *** 니 - X= (==] -4t + X" x **-[= Determine the…

Q: Consider Diagonalize A, that is, find D and X auch that A = XDX-¹. Find the general solution to the…

Q: Find sin(A), A^5, and expm(A) using (1) Cayley-Hamilton theorem and (2) Jordan decomposition given…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Rewrite the given scalar equation as a first-order system in normal form. Express the system in the…

Q: 2. For the following systems with complex eigenvalues, find the general solutions: -5 (a) x² = ( 15³…

Q: For the DE system x' = Ax Which of the following matrices corresponds to the phase portrait shown?…

A: (sorry Option First is not clear ) All Have Complex Conjugate Eigen values so All Option are…

Q: Find a (rcal) fundamental matrix for the system x' = Ax given the following A matrices. Sketch the…

A: a) A=-1-28-1 The eigen values are given by, -1-λ-28-1-λ=0⇒(λ+1)2+16=0⇒(λ+1)=±4i⇒λ=-1±4i for λ1=-1+4i…

Q: Write a'= -3x+y+ln(t), y'= t'a in matrix form as 18 31 and f(t) is 181 [*] -= P(1) [*] + f(t) where…

Q: Why can we not write the following predator prey model in matrix form X'(t) = AÑ(t)? x'(t) = ax(t) —…

Q: 4. y= cje²*+c2xe²*

A: Please see the below picture for detailed solution.

Q: (i) (3 3)-C ) - 6 3) y z 5

Q: Find A of the matrix 1- A = 2. -4 2. 1.

A: The inverse of the matrix A of order n is defined as a matrix B of order n such that AB=BA=I, where…

Q: Write the equivalent first-order system in the form of x' = Ax. Find the Coeffi- cient matrix. Also…

Q: I need help with this initial value problem using matrices: x1'= 4x1-3x2 x2'= 8x1-6x2 Initial…

Q: (a) Oë + pà + pax = (b) # + mx(1 – ±²)+ vg(x) = Asparagus(t), x(1) = -5, ±(1) = 10…

A: This is a problem of IVP.

Q: Consider the linear system 3 *' = Find the eigenvalues and eigenvectors for the coefficient matrix.…

A: The complete solutions are given below

Q: Let k be a positive integer and y be a column vector of functions with length 2k. We have the system…

Q: Express the system of differential equations in matrix notation. x" -2x+4y- (cost)x = 0 y""'+y" -tx'…

A: Given system of ODE's are in the following :To convert it equivalent system of linear ODE''s we take…

Q: Let Enter your answers in terms of the variable t. 2e³t 8e-t -4e³t+2€¯ -6e³t+ 5e-t 3e³t 20e-t Show…

A: It is given that: P=9-415-7, x1→t=2e3t-8e-t3e3t-20e-t and x2→t=-4e3t+2e-t-6e3t+5e-t

Q: x- 5y – z = 1 y -z=2 - 5z =1 1. Write the system above in Ax=b form using matrices and find the…

Q: Write in its matrix form X´=AX the following system of homogeneous linear equations:

A: Given x'1 = x1 + x2 + x3 x'2 = 2x1 - x2 -x3 x'3 = -x2 We need to write the above system in Matrix…

Q: Find the fundamental matrix for the system: x'= 9x + 12y y'= -6x9y x(0) = -2, y(0) = -6 Fundamental…

Q: of the form y₁ = x¹(1+ a₁ + a₂x² + a3x³ + ...) y2 = x2(1 + b₁x + b₂x² + b₂x³ +.. ....) where r1 >…

A: Given differential equation is 2x2y''−xy'+5x+1y=0......1. Let yx=xr∑k=0∞ckxk be the solution of the…

Q: 2. For the following systems with complex eigenvalues, find the general solutions: -5 ›× - ( 13³ ) ×…

Q: (a) Consider the system of equations 11х3 — Зх1 yi %3D - 7x1 – 6x2 – 5x3 y2 х> + 2х3 — 2х = y3…

Q: Write y – 2j + 5ý + y = = | as an autonomous system of first-order equations.

Q: y "- 3y + 2y =0 0 1 O b. ***-(2,₂3). x-(2-1) --(-) 0 1 X' 3 2 21 +-(-3) X'= 0 a. O c. O d. x x

Q: y₁' = 5y₁ + 3y2 Y2' = -6y₁4y2

Q: 2. Find fundamental (3 (a) x' = (b) x' = 2-5 4 matrices for the following systems: :)> (9) -2 62 5 3…

Q: Write the system in matrix form x' = 3x – 4y + z + t, y' = x + 2y – z + t?, z' = 6y – 7z + t3

A: A matrix equation is an equation of the form Ax = b where A is an m × n matrix, b is a vector…

Q: Let B = {(1, 3), (-2,-2)} and B' = {(-12, 0), (-4, 4)} be bases for R2, and let 23 04 A = be the…

Question

Q.1 Reduce the fourth order DE 2y“) +7y" – 9y' = -e'
with I.Cs y(0) = y'(0) = 4, y"(0) = y"(0) = -3, to the system
in the matrix form.

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

Step 2

Step 3

Step 4

Step 5

Step 6

Step by step

Solved in 6 steps with 6 images

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

Write the system in matrix form x' = 3x – 4y + z +t, y' = x + 2y – z + t?, z' = 6y – 7z + t³
A=30 ,B=20, C = |,D= 22 Find the 3x3 homogeneous matrix for 2D-reflection across a line that goes through (B, C) and makes an angle at +D degrees (counterclockwise) from the x-axis.
Use the Finite Difference method to write the equation x" + 2x' - 6x = 2, with the boundary conditions x(0) = 0 and x(9)-0 to a matrix form. Use the CD for the second order differences and the FW for the first order differences with a mesh h=3.
Convert the 3rd order homogenous ODE into a linear system of 1st order ODES and solve for y(t). у" - 4y" - 5у' %3D 0
I need the answer as soon as possible
Verify the satisfaction of the following equations y"-3y' +2y = 2x +1 with y=C,e* +C₂e²x +x+2 dy dt + 20y = 24 6 6 --e with Y=5 5 -201
Write the given linear system in matrix form. Assume X = X' = -7 3 dx dt dy dt dz dt = -7x + 8y - 9z = 3x - y = 10x + 8y + 7z 8 -9 0 -(:)) X + 0.00
X' = {(1, 2), (4, 3)} x X + {(8e3t), (12e2t)}. Where X1 = {(-e-t), (e-t)} and X2 = {(e5t), (2e5t)} are solutions of the corresponding homogeneous system. Show that the solutions of the corresponding homogeneous system are linearly independent. Find the fundamental matrix and its inverse. Solve the nonhomogeneous system given above. Show all of your work and multiply out all matrix calculations.
Need only a handwritten solution only (not a typed one).
Find two linearly independent solutions of y″+2xy=0 of the form and enter the first few coefficients shown in the photo
10