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Match the solution curve with one of the differential equations. Were Oy" + 2y' + y = 0 O 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.) 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 ßx). The differential equation should have the form y" + k²y = 0 where k = 1 so that the period of the solution is 27. The differential equation should have the form y" + k²y = 0 where k = 2 so that the period of the solution is . 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 + c₂e₂x. O The auxiliary equation should have one positive and one negative root, so that the solution has the form c₁ek₁x + c₂e-k₂x.

Match the solution curve with one of the differential equations. Were Oy" + 2y' + y = 0 O 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.) 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 ßx). The differential equation should have the form y" + k²y = 0 where k = 1 so that the period of the solution is 27. The differential equation should have the form y" + k²y = 0 where k = 2 so that the period of the solution is . 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 + c₂e₂x. O The auxiliary equation should have one positive and one negative root, so that the solution has the form c₁ek₁x + c₂e-k₂x.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 1CR
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Differential Equations

 


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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 + ₂ek₂x. 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 + ₂ek₂x. O The auxiliary equation should have one positive and one negative root, so that the solution has the form c₁ek₁× + c₂e-k₂x.
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