O y" + y 0 O y" - 5y' + 4y = 0 O y" + 2y' + 2y = 0 O y" - 3y' - 4y = 0 O y" + 2y' + y = 0 O y" + 9y = 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 ce p + C,e¯Kz*. O The differential equation should have the form y" + k²y = 0 where k = 1 so that the period of the solution is 21t. -lox -kx O The auxiliary equation should have a repeated negative root, so that the solution has the form c,e + C,xe k. The auxiliary equation should have a pair of complex roots a t 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" + y 0 O y" - 5y' + 4y = 0 O y" + 2y' + 2y = 0 O y" - 3y' - 4y = 0 O y" + 2y' + y = 0 O y" + 9y = 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 ce p + C,e¯Kz*. O The differential equation should have the form y" + k²y = 0 where k = 1 so that the period of the solution is 21t. -lox -kx O The auxiliary equation should have a repeated negative root, so that the solution has the form c,e + C,xe k. The auxiliary equation should have a pair of complex roots a t 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
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter13: Conic Sections
Section13.1: Circles
Problem 48PS
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