Question
Asked Jul 17, 2019
6 views

Differential equations.

Find the particular solutions to the given systems of equations. Please refer to attached image.

X
-())-E)
X-Gx)
1
X
, x (0) = (i)
1
1
1
-4
3
-7
X
help_outline

Image Transcriptionclose

X -())-E) X-Gx) 1 X , x (0) = (i) 1 1 1 -4 3 -7 X

fullscreen
check_circle

Expert Answer

Step 1

(a) The differential equation is given as

help_outline

Image Transcriptionclose

(5 2 -1 x, x(0)= 1 Obtain the eigenvalues for the matrix 5 A -1 det(A ) 3 1- A = 22-62+8 -(2-2)(2-4) That is, 2 and A, = 4

fullscreen
Step 2

Now obtain the eigenvectors for each of these:

help_outline

Image Transcriptionclose

For 4 2 (5-2 -1x 1-2 3 3 That is, x 3x Then for 1 3 For A 4 x1- 1-4x 5-4 3 That is, xx. Then (2) for x

fullscreen
Step 3

Thus, the general sol...

help_outline

Image Transcriptionclose

1 4t ce x =ce" Use initial condition and obtain the value of c, andc, as follows 1 1 2 C2 1 3 = -1 CC2 2 and 3c, + c, 7 3 and c2 2 2 1 4t 1 7 3 2t Therefore, the general solution is x= 2 1 3 2

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.

Related Advanced Math Q&A

Find answers to questions asked by student like you
Show more Q&A
add
question_answer

Q: I need help for number 5. There are some parts in this section that I don't understand. Please give ...

A: Problem 5.To prove that the given closed ball is closed.

question_answer

Q: Subject: Elements of Set Theory Greetings,I am really having difficult time with these problems that...

A: (a)We have to prove:

question_answer

Q: See attachment for question.

A: Click to see the answer

question_answer

Q: 2 How many subintervals does the composite trapezoid rule need to obtain the approximation of the fo...

A: Given function is 

question_answer

Q: solve (x^2y"-xy'+y=(x^2+1) using laplace transformsPlease show all your work, and do not use eulers ...

A: This is an exercise in solving differential equations by using Laplace transforms (and its propertie...

question_answer

Q: Z is a complex variable, z=x+iy

A: The z is complex variable with z = x + i y , and the given vertices are (0,0),(1,0),(1,1) and (0,1).

question_answer

Q: 3. Show that closed subspace of a complete metric space is complete. 4. Let f be a continuous mappin...

A: As per norms, the first question is answered: To prove that a closed subspace Y of a complete metric...

question_answer

Q: Find the solution to the initial value problems using integration. dH/dx=3x, H(0)=1 d2x/d2y=-9sin(y...

A: Consider first problem:

question_answer

Q: 12. The original (1999) Smash Brothers contained only 12 characters. If you play with 3 friends (4 p...

A: Hi! Since you have posted multiple question and have not mentioned which one is to be answered, i am...