Results 1 to 3 of 3

Math Help - Differential equation

  1. #1
    Newbie
    Joined
    Sep 2009
    Posts
    15

    Differential equation

    For what nonzero values of k does the function y=sin(kt) satisfy the differential equation y'' + 9y = 0?
    Last edited by mr fantastic; October 21st 2009 at 05:16 PM. Reason: Restored deleted question
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    May 2009
    Posts
    471
    Quote Originally Posted by jamessmith View Post
    For what nonzero values of k does the function y=sin(kt) satisfy the differential equation y'' + 9y = 0?

    y=\sin(kt)

     <br /> <br />
y'=k\cos(kt)<br />

     <br /> <br />
y''= -k^2\sin(kt)<br />

    y''+9y=0

     <br />
-k^2\sin(kt)+9\sin(kt)=0<br />

    And so \sin(kt)(-k^2+9)=0

    And you can solve that for k right?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Jun 2009
    From
    United States
    Posts
    676
    Thanks
    19
    Quote Originally Posted by jamessmith View Post
    For what nonzero values of k does the function y=sin(kt) satisfy the differential equation y'' + 9y = 0?
    Do you know how to get started? First just find the derivatives of y.

    y'=kcos(kt)

    y''=-k^2sin(kt)

    So just substitute into the differential equation:

    -k^2sin(kt)+9sin(kt)=0

    so k=3 is one:

    sin(kt)=0 is the other possible solution. Just find the k
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: May 8th 2011, 12:27 PM
  2. Replies: 1
    Last Post: April 11th 2011, 01:17 AM
  3. Partial differential equation-wave equation(2)
    Posted in the Differential Equations Forum
    Replies: 4
    Last Post: September 6th 2009, 08:54 AM
  4. Partial differential equation-wave equation - dimensional analysis
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: August 28th 2009, 11:39 AM
  5. Replies: 13
    Last Post: May 19th 2008, 08:56 AM

Search Tags


/mathhelpforum @mathhelpforum