Match the solution curve with one of the differential equations. 元 O y"- 5y'- 6y = 0 O y" + 4y = 0 O y" + 2y' + 2y = 0 O y" - 7y' + 12y = 0 O y" + y = 0 O y" + 2y' + y = 0 Explain your reasoning. (Assume that k, k,, and k, are all positive.) O The auxiliary equation should have two positive roots, so that the solution has the form c, eki O The auxiliary equation should have one positive and one negative root, so that the solution has the form c,e 1* + c,e¬k2X. O The differential equation should have the form y" + k²y = 0 where k = 1, so that the period of the solution is 27. The auxiliary equation should have a repeated negative root, so that the solution has the form c,e + c,xe¬x. kx O The auxiliary equation should have a pair of complex roots a t Bi where a < 0, so that the solution has the form e^(c, cos(ßx) + c, sin(Bx)). sin(ßx)). O The differential equation should have the form y" + k-y = 0 where k = 2, so that the period of the solution iS T.
Match the solution curve with one of the differential equations. 元 O y"- 5y'- 6y = 0 O y" + 4y = 0 O y" + 2y' + 2y = 0 O y" - 7y' + 12y = 0 O y" + y = 0 O y" + 2y' + y = 0 Explain your reasoning. (Assume that k, k,, and k, are all positive.) O The auxiliary equation should have two positive roots, so that the solution has the form c, eki O The auxiliary equation should have one positive and one negative root, so that the solution has the form c,e 1* + c,e¬k2X. O The differential equation should have the form y" + k²y = 0 where k = 1, so that the period of the solution is 27. The auxiliary equation should have a repeated negative root, so that the solution has the form c,e + c,xe¬x. kx O The auxiliary equation should have a pair of complex roots a t Bi where a < 0, so that the solution has the form e^(c, cos(ßx) + c, sin(Bx)). sin(ßx)). O The differential equation should have the form y" + k-y = 0 where k = 2, so that the period of the solution iS T.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Match the solution curve with one of the differential equations.
元
O y"- 5y'- 6y = 0
O y" + 4y = 0
O y" + 2y' + 2y = 0
O y" - 7y' + 12y = 0
O y" + y = 0
O y" + 2y' + y = 0
Explain your reasoning. (Assume that k, k,, and k, are all positive.)
O The auxiliary equation should have two positive roots, so that the solution has the form c, eki
O The auxiliary equation should have one positive and one negative root, so that the solution has the form c,e 1* + c,e¬k2X.
O The differential equation should have the form y" + k²y = 0 where k = 1, so that the period of the solution is 27.
The auxiliary equation should have a repeated negative root, so that the solution has the form c,e + c,xe¬x.
kx
O The auxiliary equation should have a pair of complex roots a t Bi where a < 0, so that the solution has the form e^(c, cos(ßx) + c, sin(Bx)).
sin(ßx)).
O The differential equation should have the form y" + k-y = 0 where k =
2, so that the period of the solution iS T.
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