Results 1 to 4 of 4

Math Help - Integro-Differential Equation IVP

  1. #1
    Member
    Joined
    May 2008
    Posts
    138

    Integro-Differential Equation IVP

    I need some help getting started on this problem.  y^\prime - \int\limits_{0}^{t}cos(t-\tau)y(\tau) d\tau = 1, y(0) = 2

    This problem scream Convolution to me, but the  y(\tau) is throwing me off.

    I have considered recursive integration, but am still not sure what to do with that term.

    Any help? Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Dec 2007
    From
    Anchorage, AK
    Posts
    276

    Laplace

    Considering the form of the convolution, consider taking the Laplace transform of the equation.

    --Kevin C.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member Random Variable's Avatar
    Joined
    May 2009
    Posts
    959
    Thanks
    3
    Using TwistedOne151's advice,

    let  Y(s) = \mathcal{L} [y(t)]

    then  sY(s) - y(0) - \mathcal{L} [\cos t ] \mathcal{L} [y(t)] = \frac{1}{s}

     sY(s) -2 - \frac{s}{s^{2}+1}Y(s) = \frac{1}{s}

     Y(s)\Big(\frac{s^{3}}{s^{2}+1} \Big) = \frac{1}{s} + 2

     Y(s) = \frac{s^{2}+1}{s^{4}} + 2  \ \frac{s^{2}+1}{s^{3}} = \frac{1}{s^{2}} + \frac{1}{s^{4}} + \frac{2}{s} + \frac{2}{s^{3}}

    then  y(t) = t + \frac{t^{3}}{6} + 2 + t^{2}
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    May 2008
    Posts
    138
    Thanks that was a lot easier than I thought. Makes perfect sense.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Partial Differential Equation satisfy corresponding equation
    Posted in the Differential Equations Forum
    Replies: 0
    Last Post: May 16th 2011, 08:15 PM
  2. Replies: 4
    Last Post: May 8th 2011, 01:27 PM
  3. Replies: 1
    Last Post: April 11th 2011, 02:17 AM
  4. A nonlinear integro-differential equation in 2D
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: December 30th 2009, 06:46 AM
  5. Partial differential equation-wave equation - dimensional analysis
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: August 28th 2009, 12:39 PM

Search Tags


/mathhelpforum @mathhelpforum