1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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]


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


    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]
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook