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## Homework Statement

Q) ty' + 2y = (sin t)/t, y(−π/2) = a, t < 0 . Let a

_{0}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 a

_{0}exactly.

## Homework Equations

DE

## The Attempt at a Solution

I can easily manage to get the general solution. After a series of work, I ended with y= ∏

^{2}a/4t

^{2}- cost/t

^{2}. My biggest problem here is getting a

_{0}, 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!?

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