o y" + 2y' + 2y = 0 y" + 16y = 0 o y" - 4y' + 3y = 0 y" + y = 0 y" + 2y' + y = 0 у" - Зу' — 4у 3 о Explain your reasoning. (Assume that k, k,, and k, are all positive.) The differential equation should have the form y" + k²y = 0 where k = 1 so that the period of the solution is 27. O The auxiliary equation should have two positive roots, so that the solution has the form c, ek1* + The auxiliary equation should have one positive and one negative root, so that the solution has the form c,e*1* + The auxiliary equation should have a repeated negative root, so that the solution has the form c,e + c,xe-kx. O The auxiliary equation should have a pair of complex roots a ± ßi where a < 0, so that the solution has the form ea(c, cos(ßx) + c, sin(ßx)). The differential equation should have the form y" + k
o y" + 2y' + 2y = 0 y" + 16y = 0 o y" - 4y' + 3y = 0 y" + y = 0 y" + 2y' + y = 0 у" - Зу' — 4у 3 о Explain your reasoning. (Assume that k, k,, and k, are all positive.) The differential equation should have the form y" + k²y = 0 where k = 1 so that the period of the solution is 27. O The auxiliary equation should have two positive roots, so that the solution has the form c, ek1* + The auxiliary equation should have one positive and one negative root, so that the solution has the form c,e*1* + The auxiliary equation should have a repeated negative root, so that the solution has the form c,e + c,xe-kx. O The auxiliary equation should have a pair of complex roots a ± ßi where a < 0, so that the solution has the form ea(c, cos(ßx) + c, sin(ßx)). The differential equation should have the form y" + k
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:Match the solution curve with one of the differential equations.
y 4
оу"+ 2y' + 2у %3D0
o y" + 16y = 0
o y" – 4y' + 3y = 0
o y" + y = 0
o y" + 2y' + y = 0
оу" - Зу' — 4y %3D0
Explain your reasoning. (Assume that k, k,, and k, are all positive.)
The differential equation should have the form y" + k<y = 0 where k = 1 so that the period of the solution is 27.
The auxiliary equation should have two positive roots, so that the solution has the form c, K1X + c,e*2X.
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 auxiliary equation should have a repeated negative root, so that the solution has the form c,e
-kx
+ czxe-kx,
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(ßx) + c, sin(ßx)).
O The differential equation should have the form y" + k²y = 0 where k = 2 so that the period of the solution is T.
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