Suppose the auxiliary equation of a homogeneous linear differential equation has roots m_1=-2 and m_2=±2i. What is the solution?

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.1: Solutions Of Elementary And Separable Differential Equations
Problem 10E
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Suppose the auxiliary equation of a homogeneous linear differential equation has
roots m_1=-2 and m_2=±2i.
What is the solution?
y = c,e- + Cze* cos 2x + cze* sin 2x
y = c,e-2x + c2xe2x
y = c,e-* + c, cos 2x + €z sin 2x
y = c,e-2x + Cze²x
くく
Transcribed Image Text:Suppose the auxiliary equation of a homogeneous linear differential equation has roots m_1=-2 and m_2=±2i. What is the solution? y = c,e- + Cze* cos 2x + cze* sin 2x y = c,e-2x + c2xe2x y = c,e-* + c, cos 2x + €z sin 2x y = c,e-2x + Cze²x くく
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ISBN:
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