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Finding Eigenvalues and C1 & C2

  1. Mar 19, 2012 #1
    1. The problem statement, all variables and given/known data
    (attached)


    2. Relevant equations



    3. 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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  3. Mar 19, 2012 #2

    HallsofIvy

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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 [itex]C_1= C_2= 0[/itex] and [itex]\lambda_1[/itex] and [itex]\lambda_2[/itex] can be anything. If [itex]C_1[/itex] and [itex]C_2[/itex] are not both 0, then it is a little more interesting. What can you say about the limit of [itex]e^{\lambda t}[/itex] as t goes to 0? Look at [itex]\lambda> 0[/itex] and [itex]\lambda< 0[/itex].
     
  4. Mar 19, 2012 #3
    all i can say is that lambda has to be negative for it to go 0 right?
     
  5. Mar 19, 2012 #4

    HallsofIvy

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  6. Mar 19, 2012 #5
    so i can pick any negative integer number for lambda and any integer for C1 and C2?
     
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