Results 1 to 3 of 3
Like Tree1Thanks
  • 1 Post By Soroban

Math Help - solving differential equation using integration factor

  1. #1
    Junior Member
    Joined
    Sep 2012
    From
    ohio
    Posts
    68

    solving differential equation using integration factor

    Given y' + 3y = 5te^-t. How do I get the integration factor since there is no (t) value for P(t) where (dy/dt) + P(t) = F(t). Do i divided through by t since there is a t on the righthand side? Thanks to all that for your help!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,914
    Thanks
    779

    Re: solving differential equation using integration factor

    Hello, nivek0078!

    If you truly understand the Integrating Factor,
    . . exactly where is your difficulty?

    Given: . \frac{dy}{dt} + P(y)\!\cdot\!y \:=\:Q(t)
    . . the integrating factor is: . I \:=\:e^{\int\!P(y)\,dy}



    \text{Solve: }\:\tfrac{dy}{dt}+ 3y \:=\: 5te^{-t}

    We have: . I \;=\;e^{\int\!3\,dt} \;=\;e^{3t}

    Then: . . e^{3t}\tfrac{dy}{dt} + 3e^{3t}y \;=\;5\:\!t\:\!e^{2t}

    . . . . . . . . . \frac{d}{dt}\left(e^{3t}y\right) \;=\;5\:\!t\:\!e^{2t}

    . . . . . . . . . . . . e^{3t}y \;=\;5\!\!\int\!\! t\:\!e^{2t}\,dt

    Can you finish it now?
    Thanks from nivek0078
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Sep 2012
    From
    ohio
    Posts
    68

    Re: solving differential equation using integration factor

    Yes! Thank you! That was what i was wondering about.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Solving Differential Equations with An Integrating Factor
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: May 14th 2010, 02:09 PM
  2. solving a differential equation.
    Posted in the Differential Equations Forum
    Replies: 7
    Last Post: May 13th 2010, 02:52 PM
  3. [SOLVED] differential equation given integrating factor
    Posted in the Differential Equations Forum
    Replies: 4
    Last Post: March 27th 2010, 07:05 AM
  4. Differential equation - integrating factor
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: June 19th 2009, 07:18 AM
  5. Solving differential equation
    Posted in the Calculus Forum
    Replies: 5
    Last Post: March 25th 2009, 03:09 PM

Search Tags


/mathhelpforum @mathhelpforum