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First-Order Constant-Coefficient Equations.(a)
Chapter 4, Problem 21E(choose chapter or problem)
First-Order Constant-Coefficient Equations.
(a) Substituting \(y=e^{r t}\), find the auxiliary equation for the first-order linear equation \(a y^{\prime}+b y=0\), where and
are constants with \(a \neq 0\).
(b) Use the result of part (a) to find the general solution.
Equation Transcription:
Text Transcription:
y=e^{rt}
ay'+by=0
a not=0
Questions & Answers
QUESTION:
First-Order Constant-Coefficient Equations.
(a) Substituting \(y=e^{r t}\), find the auxiliary equation for the first-order linear equation \(a y^{\prime}+b y=0\), where and
are constants with \(a \neq 0\).
(b) Use the result of part (a) to find the general solution.
Equation Transcription:
Text Transcription:
y=e^{rt}
ay'+by=0
a not=0
ANSWER:
Solution
In this question we have to find the general solution of where
Step 1
We will find the solutions in the form
(a)
Auxiliary equation for