2nd order ODE with a catch

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?

Re: 2nd order ODE with a catch

Quote:

Originally Posted by

**Lancet**

If y --> 0 as t --> +oo then C2 has to equal zero.

So you have y = C1 e^(-t) and since y(0) = a, C1 = a.

So y = a e^(-t).

Now use y'(0) = 2 to get a.

Re: 2nd order ODE with a catch

Quote:

Originally Posted by

**mr fantastic** If y --> 0 as t --> +oo then C2 has to equal zero.

So you have y = C1 e^(-t) and since y(0) = a, C1 = a.

So y = a e^(-t).

Now use y'(0) = 2 to get a.

Thank you so much for that - I just couldn't see what I was missing. In retrospect, it seems obvious, and worth kicking myself over. :)

Thanks again!

Re: 2nd order ODE with a catch

No, no, don't kick yourself. Let us do it!