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Intial-Value Problem

  1. Oct 16, 2009 #1
    1. The problem statement, all variables and given/known data

    Find an interval centered about x = 0 for which the given initial-value problem has a unique solution.

    [tex]y^{''} + (tanx)y = e^{x}[/tex]

    [tex]y(0) = 1[/tex] [tex]y^{'}(0) = 0[/tex]

    2. Relevant equations

    [tex]a_{i}(x), i=0,1,2,3,....,n[/tex] is continuous and

    [tex]a_{n} \neq 0[/tex] for every x in I.

    3. The attempt at a solution

    [tex]a_{0} = tanx[/tex] is zero at x = 0

    I am not sure if this is correct because tanx is continuous everywhere except at pi/2, 3pi/2, etc... so would interval be:

    [tex]I = (0,\infty) or (-\infty , 0)[/tex]

    or

    [tex]I = (0,\pi/2) or (-\pi/2 , 0)[/tex]
     
  2. jcsd
  3. Oct 16, 2009 #2

    Mark44

    Staff: Mentor

    How are what you have below relevant? What does ai(x) represent?
    Do you have a theorem that can be used for this problem? It might be titled Existence and Uniqueness Theorem.
     
  4. Oct 20, 2009 #3
    I found the interval:

    as tanx = sinx/cosx

    cosx can not equal zero

    so the interval is:

    [tex](-\frac{\pi}{2}, \frac{\pi}{2})[/tex]
     
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