Finding Eigenvalues and C1 & C2

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Homework Help Overview

The discussion revolves around finding eigenvalues and constants C1 and C2 in a mathematical context, likely related to differential equations or linear algebra. The original poster expresses uncertainty about how to begin the problem, particularly regarding the instruction to "choose."

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants explore the implications of the instruction to "choose," with one suggesting that it indicates an infinite number of solutions. Questions arise about the nature of eigenvalues, particularly the requirement for them to be negative, and the conditions under which constants C1 and C2 can be selected.

Discussion Status

The discussion is ongoing, with some participants providing insights into the implications of negative eigenvalues and the trivial solution. However, there is no explicit consensus on the approach to take or the specific values for C1 and C2.

Contextual Notes

Participants note that the problem lacks specific information, which may affect how they interpret the instruction to "choose." There is also a focus on the behavior of the exponential function as it relates to the eigenvalues.

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The Attempt at a Solution


I really don't know where to start. There is nothing given for me to start with. And the instruction says "Choose" so am I really suppose to really choose or do you guys any idea how to start this?

*I know that eigenvalues have to negative
 

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I suspect that the reason for the word "choose" is that there are an infinite number of solutions. For example, a "trivial" solution is C_1= C_2= 0 and \lambda_1 and \lambda_2 can be anything. If C_1 and C_2 are not both 0, then it is a little more interesting. What can you say about the limit of e^{\lambda t} as t goes to 0? Look at \lambda> 0 and \lambda< 0.
 
all i can say is that lambda has to be negative for it to go 0 right?
 
Yes.
 
so i can pick any negative integer number for lambda and any integer for C1 and C2?
 

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