Solved: (Double root) If D2 + aD + hI has distinct roots
Chapter 2, Problem 2.1.76(choose chapter or problem)
(Double root) If \(D^{2}+a D+b I\) has distinct roots \(\mu\)and \(\lambda\), show that a particular solution is \(y=\left(e^{\mu x}-e^{\lambda x}\right) /(\mu-\lambda)\). Obtain from this a solution \(x e^{\lambda x}\) by letting \(\mu \rightarrow \lambda\) and applying l'Hôpital's rule.
Text Transcription:
D^2+aD+bI
mu
lambda
y=(e^mu x - e^lambda x)/(mu-lambda)
xe^lambda x
mu rightarrow lambda
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