I have a test coming up and this is what he said to have down but its the weeken

Question

I have a test coming up and this is what he said to have down but its the weekend and I have no resources to check with to make sure I am on the right track.

1. Know the definition of a wronskian and how to use it to determine whether or not two solutions of a homogenous equation form a fundamental set. From what I found if the wronskian = 0 there is no set.

2. Know the characteristic eq. for constant coefficient problems and be able to state the three cases: b^2-4ac>0, b^2-4ac=0, b^2-4ac<0. Not sure what he means. characteristic equations are usually just used to find eigen values and vectors right.

3. How do the initial conditions determine any unknown parameters in the general solution of a nonhomogenous eq?

For 2x2 autonomous systems:

1. Know what an equilibrium solution is and how to find one or show that one does not exist. I am not sure how to find the equilibrium solution to matrices.

2. What do eigen pairs have to do with solutions of homogenous problems.

Explanation / Answer

Equilibrium Solutions

In the previous section we modeled a population based on the assumption that the growth rate would be a constant. However, in reality this doesn

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