Results 1 to 4 of 4

Math Help - Diff Eq. x' = t * cos(t)²

  1. #1
    Newbie
    Joined
    Feb 2010
    From
    Norway, Gjøvik
    Posts
    13

    Diff Eq. x' = t * cos(t)²

    Am I doing this right?

    x' = t * cos(t)²
    x = t * sin(t)²
    And that's it?
    Or should I change the "t" variable into: 0.5t², in the t in front of the sin function? As in should I derive a T, if so, which one?

    And if it says x(0) = 1, what should I do with it?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,752
    Thanks
    486
    Quote Originally Posted by ManyTimes View Post
    Am I doing this right?

    x' = t * cos(t)²
    x = t * sin(t)²
    And that's it?
    Or should I change the "t" variable into: 0.5t², in the t in front of the sin function? As in should I derive a T, if so, which one?

    And if it says x(0) = 1, what should I do with it?
    please confirm one or the other ...

    x' = t \cdot \cos(t^2)

    or

    x' = t \cdot \cos^2{t}

    ?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Feb 2010
    From
    Norway, Gjøvik
    Posts
    13
    Actually it is written without parenthesis:
    x' = t cos t²

    So my guess: x' = t cos(t²)
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,752
    Thanks
    486
    Quote Originally Posted by ManyTimes View Post
    Actually it is written without parenthesis:
    x' = t cos t²

    So my guess: x' = t cos(t²)
    dx = t\cos(t^2) \, dt

    substitution ... u = t^2 , du = 2t \, dt

    x = \frac{\sin(t^2)}{2} + C
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Diff eq IVP
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: December 10th 2009, 01:05 PM
  2. diff eqn, sin(2x).
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: March 12th 2009, 09:30 AM
  3. diff eq help
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: January 25th 2009, 01:16 PM
  4. Diff Qn'
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 29th 2008, 08:35 AM
  5. diff eq help
    Posted in the Calculus Forum
    Replies: 0
    Last Post: March 31st 2008, 03:41 PM

Search Tags


/mathhelpforum @mathhelpforum