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the solution Ilfferential equations. y4

the solution Ilfferential equations. y4

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. O y" - 3y' - 4y = 0 O y" + 2y' + y = 0 O y" + 9y = 0 O y" + y = 0 O y" + 2y' + 2y = 0 O y" - 7y' + 12y = 0 Explain your reasoning. (Assume that k, k,, and k, are all positive.) O The auxiliary equation should have one positive and one negative root, so that the solution has the form c,ekı* 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 two positive roots, so that the solution has the form c,ekı* + c,ek2*. O The differential equation should have the form y" + ky = 0 wherek = 1 so that the period of the solution is 2n. O The auxiliary equation should have a pair of complex roots a ± Bi where a < 0, so that the solution has the form eax(c, cos(Bx) + c, sin(Bx)). O The differential equation should have the form y" + k?y = 0 where k = 2 so that the period of the solution is n.
Transcribed Image Text:Match the solution curve with one of the differential equations. O y" - 3y' - 4y = 0 O y" + 2y' + y = 0 O y" + 9y = 0 O y" + y = 0 O y" + 2y' + 2y = 0 O y" - 7y' + 12y = 0 Explain your reasoning. (Assume that k, k,, and k, are all positive.) O The auxiliary equation should have one positive and one negative root, so that the solution has the form c,ekı* 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 two positive roots, so that the solution has the form c,ekı* + c,ek2*. O The differential equation should have the form y" + ky = 0 wherek = 1 so that the period of the solution is 2n. O The auxiliary equation should have a pair of complex roots a ± Bi where a < 0, so that the solution has the form eax(c, cos(Bx) + c, sin(Bx)). O The differential equation should have the form y" + k?y = 0 where k = 2 so that the period of the solution is n.
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