Results 1 to 3 of 3

Math Help - Simple second order d.e.

  1. #1
    Newbie
    Joined
    Aug 2009
    Posts
    10

    Simple second order d.e.

    Sorry about this. I've solved this equation and I'm not quite getting what I am supposed to.

    x''=-x can someone show me how to get the solution to this . Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Calculus26's Avatar
    Joined
    Mar 2009
    From
    Florida
    Posts
    1,271
    write as

    x '' + x = 0


    Assume solution of the form x = e^(rt)

    Then plugging back into the original we obtain:

    r^2e^(rt) + e^(rt) = 0

    r^2 +1 = 0

    This is the characteristic equation the solution is r = + i

    The solutions are of the form e^(it) (you only need one of the complex solutions)

    Using Euler's idenity e^(it) = cos(t) + i sin(t)

    Then the real part: cos(t) and the imaginary part : sin(t) are the solutions

    The general solution is x = Acos(t) + Bsin(t) which is easilyu verified to solve x '' + x = 0
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Rhymes with Orange Chris L T521's Avatar
    Joined
    May 2008
    From
    Chicago, IL
    Posts
    2,844
    Thanks
    3
    Quote Originally Posted by Mikey1205 View Post
    Sorry about this. I've solved this equation and I'm not quite getting what I am supposed to.

    x''=-x can someone show me how to get the solution to this . Thanks
    The characteristic equation is r^2=-1\implies r=\pm i

    Thus, the solution has the form y=c_1\cos x+c_2\sin x.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Simple first order diff. eq
    Posted in the Differential Equations Forum
    Replies: 4
    Last Post: May 28th 2011, 05:20 AM
  2. non homogeneous second order, should be simple
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: February 24th 2010, 07:16 PM
  3. No simple groups of order 48
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: March 18th 2009, 08:17 PM
  4. Simple Group order 168
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: October 2nd 2008, 07:02 PM
  5. Simple one on first-order linear DEs
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 23rd 2008, 12:32 PM

Search Tags


/mathhelpforum @mathhelpforum