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)).

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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