Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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].


    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)\,.

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