Given the IVP
1.) Find sol'n of the IVP in terms of
2.) Find such that as the sol'n approached zero.
First, we find the auxiliary equation by the quadratic.
This gives us:
Now, by using y(0)=2, we can find C1:
Then using the other IC, we can find C2:
Therefore, the IVP in terms of a is:
Now, find the limit for the last portion of the problem. It should be kind of easy to see what a is now.
What is the limit on the right when x is unbounded?. What will give 0?