Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Match the solution curve with one of the differential equations. x y"- 7y' +12y = 0 Ⓒy" + 4y = 0 Ⓒy" + y = 0 Oy" + 2y' + y = 0 y" - 5y' - 6y = 0 y" + 2y' + 2y = 0 X Explain your reasoning. (Assume that k, k₁, and k₂ are all positive.) The auxiliary equation should have two positive roots, so that the solution has the form c₁ek1* + c₂ek₂x. The differential equation should have the form y" + k²y = 0 where k = 1, so that the period of the solution is 21. The auxiliary equation should have one positive and one negative root, so that the solution has the form c₁e1* + c₂e-k₂x. The auxiliary equation should have a repeated negative root, so that the solution has the form c,e-x + exe k The differential equation should have the form y" + k²y = 0 where k = 2, so that the period of the solution is I. The auxiliary equation should have a pair of complex roots a ± ßi where a < 0, so that the solution has the form eax (c₁ cos(x) + C₂ sin(x)). X

Match the solution curve with one of the differential equations. x y"- 7y' +12y = 0 Ⓒy" + 4y = 0 Ⓒy" + y = 0 Oy" + 2y' + y = 0 y" - 5y' - 6y = 0 y" + 2y' + 2y = 0 X Explain your reasoning. (Assume that k, k₁, and k₂ are all positive.) The auxiliary equation should have two positive roots, so that the solution has the form c₁ek1* + c₂ek₂x. The differential equation should have the form y" + k²y = 0 where k = 1, so that the period of the solution is 21. The auxiliary equation should have one positive and one negative root, so that the solution has the form c₁e1* + c₂e-k₂x. The auxiliary equation should have a repeated negative root, so that the solution has the form c,e-x + exe k The differential equation should have the form y" + k²y = 0 where k = 2, so that the period of the solution is I. The auxiliary equation should have a pair of complex roots a ± ßi where a < 0, so that the solution has the form eax (c₁ cos(x) + C₂ sin(x)). X

Advanced Engineering Mathematics
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
icon
Related questions
Question
Match the solution curve with one of the differential equations. x y" - 7y' + 12y = 0 Ⓒy" + 4y = 0 Ⓒy" + y = 0 Oy" + 2y' + y = 0 y" - 5y' - 6y = 0 y" + 2y + 2y = 0 X Explain your reasoning. (Assume that k, k₁, and k₂ are all positive.) The auxiliary equation should have two positive roots, so that the solution has the form c₂₁ek₁x + ₂k₂x. The differential equation should have the form y" + k²y = 0 where k = 1, so that the period of the solution is 21. The auxiliary equation should have one positive and one negative root, so that the solution has the form c₁ek1* + c₂e-k₂x. The auxiliary equation should have a repeated negative root, so that the solution has the form c₂e-x + EXe k The differential equation should have the form y" + k²y = 0 where k = 2, so that the period of the solution is I. 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(x) + C₂ sin(x)). X
Transcribed Image Text:Match the solution curve with one of the differential equations. x y" - 7y' + 12y = 0 Ⓒy" + 4y = 0 Ⓒy" + y = 0 Oy" + 2y' + y = 0 y" - 5y' - 6y = 0 y" + 2y + 2y = 0 X Explain your reasoning. (Assume that k, k₁, and k₂ are all positive.) The auxiliary equation should have two positive roots, so that the solution has the form c₂₁ek₁x + ₂k₂x. The differential equation should have the form y" + k²y = 0 where k = 1, so that the period of the solution is 21. The auxiliary equation should have one positive and one negative root, so that the solution has the form c₁ek1* + c₂e-k₂x. The auxiliary equation should have a repeated negative root, so that the solution has the form c₂e-x + EXe k The differential equation should have the form y" + k²y = 0 where k = 2, so that the period of the solution is I. 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(x) + C₂ sin(x)). X
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
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,
SEE MORE TEXTBOOKS