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.
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!?