Results 1 to 2 of 2

Math Help - Reduction of order

  1. #1
    Junior Member
    Joined
    May 2010
    Posts
    74

    Reduction of order

    (t)d^2y/dt^2 - (t+1)dy/dy + y = t^2
    y1(t) = e^t y2(t) = t + 1

    I have to do this is 2 different methods the first method was using variation of parameters which I could do but then when it came to using reduction of order I kept getting stuck half way.

    The first thing i did was let y = ue^t then i differentiated and subbed back intothe equation then it was u absent which let me use p = du/dt and dp/dt = d^2u/dt^2 then i got P = tc/(e^t -t) where c is a constant then i couldnt integrate that to find u.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member DeMath's Avatar
    Joined
    Nov 2008
    From
    Moscow
    Posts
    473
    Thanks
    5
    Quote Originally Posted by CookieC View Post
    (t)d^2y/dt^2 - (t+1)dy/dy + y = t^2
    y1(t) = e^t y2(t) = t + 1

    I have to do this is 2 different methods the first method was using variation of parameters which I could do but then when it came to using reduction of order I kept getting stuck half way.

    The first thing i did was let y = ue^t then i differentiated and subbed back intothe equation then it was u absent which let me use p = du/dt and dp/dt = d^2u/dt^2 then i got P = tc/(e^t -t) where c is a constant then i couldnt integrate that to find u.
    Rewrite your equation in this form \displaystyle{\frac{t(y''-y')-(y'-y)}{t^2}=1}

    Then \displaystyle{\left(\frac{y'-y}{t}\right)'=(t+C)'~\Rightarrow~\frac{y'-y}{t}=t+C~\Rightarrow~y'-y=t^2+Ct}
    Last edited by DeMath; September 2nd 2010 at 05:11 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. 2nd Order, Homog., Reduction of Order
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: November 27th 2011, 06:36 AM
  2. Reduction of Order
    Posted in the Differential Equations Forum
    Replies: 5
    Last Post: April 1st 2011, 09:31 AM
  3. Reduction of Order
    Posted in the Differential Equations Forum
    Replies: 4
    Last Post: April 24th 2010, 07:21 AM
  4. Reduction of Order
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: November 2nd 2009, 04:33 PM
  5. Replies: 4
    Last Post: August 12th 2008, 04:46 AM

Search Tags


/mathhelpforum @mathhelpforum