Results 1 to 4 of 4

Math Help - linear homogenous equation, simple question.

  1. #1
    Member
    Joined
    Jan 2008
    Posts
    175

    linear homogenous equation, simple question.

    determine the longest interval in which the given initial value problem is certain to have a unique twice differentiable solution without finding the solution.


    ty" + 3y = t, y(1) = 1, y'(1)=2

    i set this up and got

    y" + (3/t)y = 1


    the interval in the book says its 0< t< infinity, but im not understanding that.
    When I look at q(t) = (3/t) it looks like it would have a continuous solution everywhere except zero. why are they truncating the negative?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    tah
    tah is offline
    Junior Member
    Joined
    Feb 2009
    Posts
    51
    Hi, it says the longest interval right and  ]-\infty,0[\cup]0,\infty[ isn't one.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Jan 2008
    Posts
    175
    no its just 0 -> infinity.

    im not really understanding the logic.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by p00ndawg View Post
    determine the longest interval in which the given initial value problem is certain to have a unique twice differentiable solution without finding the solution.


    ty" + 3y = t, y(1) = 1, y'(1)=2

    i set this up and got

    y" + (3/t)y = 1


    the interval in the book says its 0< t< infinity, but im not understanding that.
    When I look at q(t) = (3/t) it looks like it would have a continuous solution everywhere except zero. why are they truncating the negative?
    your initial data is given at t = 1. thus, you want to be on the right side of zero. y(1) would make no sense otherwise. so the largest continuous interval for your solution is t > 0
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Simple question for linear first-order differential equation. I can't move on!
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: September 17th 2011, 06:06 PM
  2. Quick Simple homogenous equation help
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: May 6th 2010, 09:35 PM
  3. Replies: 2
    Last Post: March 31st 2010, 01:24 AM
  4. Simple question regarding linear equation ?
    Posted in the Algebra Forum
    Replies: 2
    Last Post: November 13th 2008, 01:45 AM
  5. Non Linear homogenous differential equation
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 28th 2008, 06:44 AM

Search Tags


/mathhelpforum @mathhelpforum