Find all values of for which the differential equation has
Chapter 16, Problem 26(choose chapter or problem)
Solutions of a Differential Equation Find all values of k for which the differential equation
y’’ + 2ky’ + ky = 0
has a general solution of the indicated form.
(a) \(y=C_{1} e^{m_{3} x}+C_{2} e^{m_{2} x}\)
(b) \(y=C_{1} e^{m_{1} x}+C_{2} x e^{m_{1} x}\)
(c) \(y=C_{1} e^{\alpha x} \cos \beta x+C_{2} e^{\alpha x} \beta x\)
Text Transcription:
y=C_1 e^m_3 x + C_2 e^m_2 x
y=C_1 e^m_a x + C_2 xe^m_1 x
y=C_1 e^alpha x cos beta x + C_2 e^alpha x beta x
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