Match the solution curve with one of the differential equations. y" + 2y' + 2y = 0 o y" + 2y' + y = 0 o y" + 4y = 0 o y" - 2y' - 3y = 0 y" – 4y' + 3y = 0 y" + y = 0 Explain your reasoning. (Assume that k, k,, and k, are all positive.) The differential equation should have the form y" + ky = 0 where k = 2, so that the period of the solution is r. The auxiliary equation should have a repeated negative root, so that the solution has the form c,e -kx + C2xe -kx The auxiliary equation should have two positive roots, so that the solution has the form c,eki* + c,eK2X. The auxiliary equation should have one positive and one negative root, so that the solution has the form c, ek1x + Cze¬k2x. The differential equation should have the form y" + ky = 0 where k = 1, so that the period of the solution is 2z. The auxiliary equation should have a pair of complex roots a ± ßi where a < 0, so that the solution has the form eax(c, cos(ßx) + c, sin(ßx)).
Match the solution curve with one of the differential equations. y" + 2y' + 2y = 0 o y" + 2y' + y = 0 o y" + 4y = 0 o y" - 2y' - 3y = 0 y" – 4y' + 3y = 0 y" + y = 0 Explain your reasoning. (Assume that k, k,, and k, are all positive.) The differential equation should have the form y" + ky = 0 where k = 2, so that the period of the solution is r. The auxiliary equation should have a repeated negative root, so that the solution has the form c,e -kx + C2xe -kx The auxiliary equation should have two positive roots, so that the solution has the form c,eki* + c,eK2X. The auxiliary equation should have one positive and one negative root, so that the solution has the form c, ek1x + Cze¬k2x. The differential equation should have the form y" + ky = 0 where k = 1, so that the period of the solution is 2z. The auxiliary equation should have a pair of complex roots a ± ßi where a < 0, so that the solution has the form eax(c, cos(ßx) + c, sin(ßx)).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:Match the solution curve with one of the differential equations.
y
o y" + 2y' + 2y = 0
o y" + 2y' + y =
o y" + 4y = 0
o y" - 2y' – 3y = 0
o y" - 4y' + 3y = 0
o y" + y = 0
Explain your reasoning. (Assume that k, k,, and k, are all positive.)
The differential equation should have the form y" + ky
= 0 where k = 2, so that the period of the solution is a.
-kx
O The auxiliary equation should have a repeated negative root, so that the solution has the form c,e
+ c2xe-kx.
O The auxiliary equation should have two positive roots, so that the solution has the form c, ek1× + c,e*2*.
O The auxiliary equation should have one positive and one negative root, so that the solution has the form c,ek1× + c,e¬k2x.
O The differential equation should have the form y" + k<y = 0 wherek = 1, so that the period of the solution is 27.
O The auxiliary equation should have a pair of complex roots a + ßi where a < 0, so that the solution has the form eax(c, cos(Bx) + c, sin(ßx)).
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
