# A de critical value problem!

1. Oct 2, 2013

### ehabmozart

1. The problem statement, all variables and given/known data

Q) ty' + 2y = (sin t)/t, y(−π/2) = a, t < 0 . Let a0 be
the value of a for which the transition from one type of behavior to another occurs.Solve the IVP and find the critical value a0 exactly.

2. Relevant equations

DE

3. The attempt at a solution

I can easily manage to get the general solution. After a series of work, I ended with y= ∏2a/4t2 - cost/t2 . My biggest problem here is getting a0, the critical value. I mean what is exactly the critical value. In this case I cannot equate y' to be zero. I want a general explanation on what the critical value means!?

Last edited: Oct 2, 2013
2. Oct 2, 2013

### szynkasz

Consider $\lim\limits_{t\to 0}y(t)$ in dependence on $a$