I have an odd ODE question that I could use a hand with...

----------------

Find "a" so that the solution approaches 0 as t approaches infinity.

----------------

So here's what I've done:

So, unless I've made a mistake somewhere, I've done most of the work. But I don't understand how I can get an "a" that will cause the solution to approach 0 as t approaches infinity. Since the second term is not part of a fraction, I'm not sure how this can be done.

Can someone help me to understand what I'm missing?