4. Find the general solution of the system of differential equations 15 8 -4 d. 4 11 4 x+ 14 X%3D dt 4 7 Hint: The characteristic polynomial of the coefficient matrix is -(A – 3)(A – 11)( – 19). Moreover 1 X,(t) = -2 %3D 1 1

4. Find the general solution of the system of differential equations 15 8 -4 d. 4 11 4 x+ 14 X%3D dt 4 7 Hint: The characteristic polynomial of the coefficient matrix is -(A – 3)(A – 11)( – 19). Moreover 1 X,(t) = -2 %3D 1 1

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: Let A be a constant 4 x 4 matrix. It is know that the general solution of a system of linear…

A: A matrix is said to be diagonalizable if Algebraic multiplicity of eigen values = geometric…

Q: . Let A = -1 -1)· (a) Find a fundamental set of real solutions and hence a real fur F(t) of r' = Ar.…

A: Given A = -32-1-1

Q: Write the standard form of the equation and the general form of the equation of the circle with…

Q: OF PARAMETERS to find b. Use the method of VARIATION the general solution of the following system of…

A: Consider the given systemThe eigen values of the coefficient matrix are with corresponding eigen…

Q: of A By computing the fundamental matrix, show that the matrix exponential is eAt = (¹ 1 + 2t t -4t…

A: We have to find the matrix exponent of A.

Q: Write the given linear system in matrix form. Assume X = dx dt dy dt dz dt -()) -2x + 4y + e-t…

Q: Solve the initial value problem for the homoge- neous system of differential equations (:)- d 12 5 3…

Q: Could you solve the problem completely using linear algebra handwritten?

Q: 3. Find the general solution of the system of differential equations d X = dt 8 -5 X 10 cos(7t) – 7…

A: Given: ddt(x)=8-5106x+4t3e7tcos(7t)-7sin(7t)10cos(7t)+8t7e7t7cos(7t)-sin(7t)10sin(7t) Here A=8-5106

Q: nd the general solution of the system x'(t) = Ax(t) for the - 1 1 A = 1 8 1 0 - 21 - 1 %3D

A: x(t)=c1e-t-101+c2e3t-1-421+c3e4t-1-521

Q: 1. Find the general solution of the system of differential equations d X = dt 9 -4 х. 5 Hint: The…

Q: 6. Find the general solution of the system of differential equations -B -B -3 -B -B d B х, - dt…

A: Find the general solution of the system of differential equations: ddtX=α-β-β-βα-β-β-βαX, where α=0…

Q: :). d 8 -5 X%= dt 10 lint: The characteristic polynomial of the coefficient matrix is X2 – 14A + 98.…

Q: 8

Q: 5. Find the general solution of the system of differential equations 2 d -2 11 7 х. dt -7 -3 Hint:…

A: We solve the given system of differential equations by finding eigenvalues and corresponding…

Q: 3. Find the general solution of the system of differential equations d X = dt 8. -5 10 cos(7t) – 7…

Q: 2 2 1 2 5 2 1 2 2 dt 2 (3) 1 + 6t°e + 7t°e? -1 -1 + 8t'et 1 Hint: The characteristic polymomial of…

Q: Question 2.7b. Consider the linear system of differential equations x = 4x-6y Which of these is NOT…

Q: -2 1 1 Write 3 Problem 1. Solve the initial value problem X(t) = X(t), where X (0) = your -5 4 final…

Q: Suppose that for a 2 x 2 matrix A, AŬ= 3õ for ū = How is the pair (3, v) called for a matrix A?…

A: given a matrix A of order 2×2 , Av→=3v→ for v→=-1-1 (a) how is the pair 3,v→ called for a matrix A…

Q: 6. Find the general solution of the system of differential equations a -8 -B -8 -8 -B d -8 x, where…

A: Given the system of differential equation is ddtx=α-β-β-βα-β-β-βαx

Q: 3. Find the general solution of the system of differential equations d. 8 -5 = x* cos(7t) – 7…

Q: Let 9 P = 15 2e3t – 6e 3et – -4e3t + 2e -6e3t + 5e¯ ỹ1(t) [3e - 15e+| V2(t) = a. Show that j1 (t) is…

Q: Use the method of UNDETERMINED find the general solution of the following system of DEs:…

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

4. Find the general solution of the system of differential equations
()
15 8
-4
d.
4
11
4
x+
14
X%3D
dt
4
7
Hint: The characteristic polynomial of the coefficient matrix is -(A – 3)(A – 11)( – 19).
Moreover
1
X,(t) =
-2
%3D
1
1
is a particular solution of the system.

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 by step

Solved in 5 steps with 5 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Differential Equation$

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

4. Solve the non-homogeneous systems of ODEs x' = Ax+f(t), with x(a) = xa using the given matrix exponentials. 4 -1 - ( 1 = ₂ ), !), f(t) = f(t) = ( 5 -2 (a) A = 18e2t 30e²t ), x(0) = ( 0 ), e4t. At = 1 ( -e-t + 5e³t -5e-t +5e³t e-t-e³t 5e-t e³t
1. for the case of repeated real roots what would the general solution be?2. if i was to let y1(t) = theta(t) as well as y2(t) = theta'(t)=y1'(t) how could i show that the initial equation could be written as a system of 1st order odes that involved y1 and y2. the system will then need to be presented as a the matrix equation y' = My
Solve the nonhomogeneous system of differential equations 8 -2 2 8 d -2 8 2|x - - e2t| 16 dt 2 8 24 Hint: The characteristic polynomial of the coefficient matrix is -(A – 10)²(A – 4).
10
1.10 Given any m × n matrices A and B, solve the matrix equation 3(X + ½ A) = 5(X − 2(B). -
10. Find the general solution of the system of differential equations 3 -2 -2 d. X = -3 -2 -6 X dt 3 10 1 + 2tet + 3t?et + 4t°et 3 1 -3 Hint: The characteristic polymomial of the coefficient matrix is -(A- 4)²(A- 3). Moreover (:) 2 1 Xp(t) = t²et +t³et +t'e3t -1 -1 -3 is a particular solution of the system.
Which one of the following is the characteristic equation of the matrix (1 − A)² (5 — A) = 0 (1 – A²)(5 — A) = 0 (1 − A)(5 — X) = 0 (1 − A)(5 — A)² = 0 2 0 7 1 3 0 7 4 ?
Consider the second-order system of differential equations dy d²x dt² =x-5y, The coefficient matrix 1 -5 eigenvalues are 6 and -4. Select the option that gives the general solution of this system. I dt² C₁ -5x + y. 1 -5 11 1 has eigenvectors Select one: [*] = C₁ [ ¹₁ ] cos(√õt) + C₂ [ ¹₁ ] sin(√6t) + Cs [1] cos(2t) + C₁ [1] C3 C4 sin(2t) evot + Vot C3 - [3] = a₁ [¹₁] ev [*] = C₁ [1] cos(√ēt) + C₂ H ₂[1] HHHHH [+] = C₁₂ [ ¹₁ ] ev√² + C₂ [ ¹₁ ] e-√₂ 3 [1] 2²¹ -C₂₁ [ ²₁ ] e-√² + C₂ [1] sin(√6t) + C3 [1₁] [1] Cos evot +03 e2t+CA C₂ [4] [1] and H cos(√6t) + C₂ and the corresponding cos(2t) + C4 H e2t + C4 sin(2t) -2t [¹1] e ²2 -2t e2t sin (√6t) + C3 as He" + a₁₂H₁² -2t
7
3
9
Chapter 2, Section 2.2, Additional Question 01 Solve the given differential equation. 7x - 1 y 7+ 5y 5 y+ 7 - x+c 7y + 7 = -X + C 7y +y = 7x - x+c 5 7y + 7 * -x+c 7 7y + 5y? = . - x+c 3*