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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)).

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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Match the solution curve with one of the differential equations. y o y" + 2y' + 2y = 0 o y" + 2y' + y = o y" + 4y = 0 o y" - 2y' – 3y = 0 o y" - 4y' + 3y = 0 o 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 a. -kx O The auxiliary equation should have a repeated negative root, so that the solution has the form c,e + c2xe-kx. O The auxiliary equation should have two positive roots, so that the solution has the form c, ek1× + c,e*2*. O 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 differential equation should have the form y" + k<y = 0 wherek = 1, so that the period of the solution is 27. 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(Bx) + c, sin(ßx)).
Transcribed Image Text:Match the solution curve with one of the differential equations. y o y" + 2y' + 2y = 0 o y" + 2y' + y = o y" + 4y = 0 o y" - 2y' – 3y = 0 o y" - 4y' + 3y = 0 o 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 a. -kx O The auxiliary equation should have a repeated negative root, so that the solution has the form c,e + c2xe-kx. O The auxiliary equation should have two positive roots, so that the solution has the form c, ek1× + c,e*2*. O 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 differential equation should have the form y" + k<y = 0 wherek = 1, so that the period of the solution is 27. 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(Bx) + c, sin(ßx)).
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