Finding Eigenvalues and C1 & C2

[DrunkApple]

Homework Statement

(attached)

Homework Equations

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

 

[HallsofIvy]

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 $\lambda< 0$.

 

[DrunkApple]

all i can say is that lambda has to be negative for it to go 0 right?

 

[HallsofIvy]

Yes.

 

[DrunkApple]

so i can pick any negative integer number for lambda and any integer for C1 and C2?