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Match the solution curve with one of the differential equations. Whene 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. 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.

Match the solution curve with one of the differential equations. Whene 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. 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
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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SET M3

Differential Equations

 


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- Higher Order Differential Equation

 


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Match the solution curve with one of the differential equations. tiforme 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 + c₂e₂x. 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. tiforme 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 + c₂e₂x. 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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