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A de critical value problem!

  • Thread starter ehabmozart
  • Start date
  • #1
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Homework Statement



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.

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= ∏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:

Answers and Replies

  • #2
115
2
Consider ##\lim\limits_{t\to 0}y(t)## in dependence on ##a##
 

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