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Match the solution curve with one of the differential equations. O y" + 2y' + 2y = 0 O y" – 7y' + 12y = 0 O y" + 2y' + y = 0 O y" – 4y' – 5y = 0 O y" + y = 0 O y" + 4y = 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,eki* + c,e' The differential equation should have the form y" + k?y = 0 where k = 1, so that the period of the solution is 2n. The auxiliary equation should have two positive roots, so that the solution has the form c, ek1* + c,ek2x. O The auxiliary equation should have a repeated negative root, so that the solution has the form c,e-kx + c,xe-kx. O The differential equation should have the form y" + k2y = 0 where k = 2, so that the period of the solution is n. O The auxiliary equation should have a pair of complex roots a ± ßi where a < 0, so that the solution has the form ex(c, cos(ßx) + c, sin(Bx)).

Match the solution curve with one of the differential equations. O y" + 2y' + 2y = 0 O y" – 7y' + 12y = 0 O y" + 2y' + y = 0 O y" – 4y' – 5y = 0 O y" + y = 0 O y" + 4y = 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,eki* + c,e' The differential equation should have the form y" + k?y = 0 where k = 1, so that the period of the solution is 2n. The auxiliary equation should have two positive roots, so that the solution has the form c, ek1* + c,ek2x. O The auxiliary equation should have a repeated negative root, so that the solution has the form c,e-kx + c,xe-kx. O The differential equation should have the form y" + k2y = 0 where k = 2, so that the period of the solution is n. O The auxiliary equation should have a pair of complex roots a ± ßi where a < 0, so that the solution has the form ex(c, cos(ßx) + c, sin(Bx)).

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" + 2y' + 2y = 0 O y" – 7y' + 12y = 0 О у" + 2y' +у %3D 0 О у" - 4y' - 5у %3D0 O y" + y = 0 O y" + 4y = 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. + The differential equation should have the form y" + k?y = 0 where k = 1, so that the period of the solution is 2n. O The auxiliary equation should have two positive roots, so that the solution has the form c,ekı* + c,ek2*. O The auxiliary equation should have a repeated negative root, so that the solution has the form + O The differential equation should have the form y" + k?y = 0 where k = 2, so that the period of the solution is T. 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(Bx)).
Transcribed Image Text:Match the solution curve with one of the differential equations. O y" + 2y' + 2y = 0 O y" – 7y' + 12y = 0 О у" + 2y' +у %3D 0 О у" - 4y' - 5у %3D0 O y" + y = 0 O y" + 4y = 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. + The differential equation should have the form y" + k?y = 0 where k = 1, so that the period of the solution is 2n. O The auxiliary equation should have two positive roots, so that the solution has the form c,ekı* + c,ek2*. O The auxiliary equation should have a repeated negative root, so that the solution has the form + O The differential equation should have the form y" + k?y = 0 where k = 2, so that the period of the solution is T. 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(Bx)).
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