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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 & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.4: Plane Curves And Parametric Equations
Problem 24E
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MARR 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 pX + C,e¯Kz*. O The differential equation should have the form y" + k´y = 0 where k = 1 so that the period of the solution is 21t. -kx O The auxiliary equation should have a repeated negative root, so that the solution has the form c,e + C,xe kx. The auxiliary equation should have a pair of complex roots a ± ßi where a < 0, so that the solution has the form ea(c, cos(ßx) + c, sin(ßx)). O The differential equation should have the form y" + k<y =0 where k = 2 so that the period of the solution is Tt. P The auxiliary equation should have two positive roots, so that the solution has the form c,e1* + c,e%2*.
Transcribed Image Text:MARR 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 pX + C,e¯Kz*. O The differential equation should have the form y" + k´y = 0 where k = 1 so that the period of the solution is 21t. -kx O The auxiliary equation should have a repeated negative root, so that the solution has the form c,e + C,xe kx. The auxiliary equation should have a pair of complex roots a ± ßi where a < 0, so that the solution has the form ea(c, cos(ßx) + c, sin(ßx)). O The differential equation should have the form y" + k<y =0 where k = 2 so that the period of the solution is Tt. P The auxiliary equation should have two positive roots, so that the solution has the form c,e1* + c,e%2*.
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