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Higher order General Method problem

  1. Sep 10, 2006 #1
    hi guys!

    okz this is a question from Higher Order Differential Equations. We are solving it from General Method to find [tex]y_{p}[/tex].

    [tex]y_{p}=\frac{secax}{D^{2}+a^{2}}[/tex]

    I solve it and reaches this point:

    [tex]y_{p}=\frac{1}{D+a\iota} e^{a\iota x} \int secax.e^{-a\iota x} dx[/tex]

    Please tell me some way to deal with this Integral Term. How can i solve it to get the final answer. What should be the best way to solve it,

    i shall be thankful to u for this act of kindness.

    take carez!!
     
    Last edited: Sep 10, 2006
  2. jcsd
  3. Sep 12, 2006 #2
    What is the range of x? Are you solving for some particular range or the whole x-axis?
    If the integral has upper and lower limits then it looks easier, particularly if you're integrating from [tex]-\infty[/tex] to [tex]\infty[/tex].
    By the way, is [tex]\iota[/tex] some parameter, or [tex]\iota^2=-1[/tex]?
     
    Last edited: Sep 12, 2006
  4. Sep 13, 2006 #3
    thanks for ur interest!

    there are no limits in this question

    the letter i is basically iota!
     
  5. Sep 13, 2006 #4
    In that case the integral is straightforward:

    [tex]sec\left(ax\right)e^{-iax} &=& \frac{\cos\left(ax\right)-i\sin\left(ax\right)}{\cos(ax)}
    \\
    &=& 1 - i\tan\left(ax\right)\,.
    [/tex]

    These are just standard integrals....
     
  6. Sep 13, 2006 #5
    (By the way my last post is assuming [if I understood correctly from what you said], that [tex]\iota=i[/tex]).
     
  7. Sep 14, 2006 #6
    yeah thats true jpr0

    thanks for ur help!
     
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