Match the solution curve with one of the differential equations. Whe y" + 2y' + y = 0 y" + 9y = 0 Oy" - 3y' + 2y = 0 Oy" + 2y' + 2y = 0 Oy" - 3y' - 4y = 0 Oy"+y=0 Explain your reasoning. (Assume that k, k₁, and k₂ are all positive.) O The auxiliary equation should have a pair of complex roots a ± ßi where a < 0, so that the solution has the form ex (c₁ cos ẞx + c₂ sin x). The differential equation should have the form y" + k²y = 0 where k = 1 so that the period of the solution is 27. O The differential equation should have the form y" + k²y = 0 where k = 2 so that the period of the solution is é. O The auxiliary equation should have a repeated negative root, so that the solution has the form c₁e-kx + c₂xe-kx O The auxiliary equation should have two positive roots, so that the solution has the form c₁ek₁x + c₂ek₂x O The auxiliary equation should have one positive and one negative root, so that the solution has the form c₁ek₁x + c₂e-K₂x.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question

SET M4

Differential Equations

 


Note: If you have already answered the problems in this post, kindly ignore it. If not, then answer it. Thank you, Tutor!

 


Content Covered:

- Higher Order Differential Equation

 


Directions: 

Answer the problem below by showing the complete solution.  In return, I will give you a good rating. Thank you so much!

 


Note: Please be careful with the calculations in the problem. Kindly double check the solution and answer if there is a deficiency. And also, box the final answer.

 


Thank you so much!

Match the solution curve with one of the differential equations.
Where
Oy" + 2y' + y = 0
Oy" + 9y = 0
Oy" - 3y' + 2y = 0
Oy"+ 2y' + 2y = 0
Oy" - 3y' 4y = 0
Oy" + y = 0
Explain your reasoning. (Assume that k, k₁, and k₂ are all positive.)
O The auxiliary equation should have a pair of complex roots a ± ßi where a < 0, so that the solution has the form ex(c₁ cos ẞx + c₂ sin ẞx).
O The differential equation should have the form y" + k²y = 0 where k = 1 so that the period of the solution is 2.
The differential equation should have the form y" + k²y = 0 where k = 2 so that the period of the solution is T.
O The auxiliary equation should have a repeated negative root, so that the solution has the form c₁e-kx + c₂xe-kx
O The auxiliary equation should have two positive roots, so that the solution has the form c₁ek₁x + c₂ek₂x.
O The auxiliary equation should have one positive and one negative root, so that the solution has the form c₁ek₁× + c₂e-k₂x.
Transcribed Image Text:Match the solution curve with one of the differential equations. Where Oy" + 2y' + y = 0 Oy" + 9y = 0 Oy" - 3y' + 2y = 0 Oy"+ 2y' + 2y = 0 Oy" - 3y' 4y = 0 Oy" + y = 0 Explain your reasoning. (Assume that k, k₁, and k₂ are all positive.) O The auxiliary equation should have a pair of complex roots a ± ßi where a < 0, so that the solution has the form ex(c₁ cos ẞx + c₂ sin ẞx). O The differential equation should have the form y" + k²y = 0 where k = 1 so that the period of the solution is 2. The differential equation should have the form y" + k²y = 0 where k = 2 so that the period of the solution is T. O The auxiliary equation should have a repeated negative root, so that the solution has the form c₁e-kx + c₂xe-kx O The auxiliary equation should have two positive roots, so that the solution has the form c₁ek₁x + c₂ek₂x. O The auxiliary equation should have one positive and one negative root, so that the solution has the form c₁ek₁× + c₂e-k₂x.
Expert Solution
steps

Step by step

Solved in 4 steps with 25 images

Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,