Results 1 to 5 of 5

Math Help - unbound solution

  1. #1
    Member
    Joined
    Jan 2011
    Posts
    83
    Thanks
    1

    unbound solution

    for an ordinary differential equation y" + py' +(p^2/4) y =0
    there exist a unbounded solution y(x)

    limit x->infinite |y(x)/x| exist.

    can anyone explain how the unbounded solution exist.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,513
    Thanks
    1404

    Re: unbound solution

    Quote Originally Posted by saravananbs View Post
    for an ordinary differential equation y" + py' +(p^2/4) y =0
    there exist a unbounded solution y(x)

    limit x->infinite |y(x)/x| exist.

    can anyone explain how the unbounded solution exist.
    Is p a constant or a function of x?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Jan 2011
    Posts
    83
    Thanks
    1

    Re: unbound solution

    p is a constant.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,513
    Thanks
    1404

    Re: unbound solution

    Well then the characteristic equation would be \displaystyle \begin{align*} m^2 + p\,m + \frac{p^2}{4} &= 0 \end{align*}. Solving for m gives

    \displaystyle \begin{align*} m^2 + p\,m + \frac{p^2}{4} &= 0 \\ \left(m + \frac{p}{2}\right)^2 &= 0 \\ m + \frac{p}{2} &= 0 \\ m &= -\frac{p}{2} \end{align*}

    Since this is a repeated root, the solution to your DE is \displaystyle \begin{align*} y = A\,e^{-\frac{p}{2}x} + B\,x\,e^{-\frac{p}{2}x} \end{align*}.

    Now you should be able to evaluate \displaystyle \begin{align*} \lim_{x \to \infty}\left|\frac{y}{x}\right| \end{align*}.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Jan 2011
    Posts
    83
    Thanks
    1

    Re: unbound solution

    is the answer is zero. when x-->infinite
    Last edited by saravananbs; May 13th 2012 at 06:02 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: September 23rd 2011, 03:39 AM
  2. General Solution of a differential solution
    Posted in the Differential Equations Forum
    Replies: 4
    Last Post: September 11th 2010, 02:49 AM
  3. Replies: 1
    Last Post: March 24th 2010, 12:14 AM
  4. Finding the general solution from a given particular solution.
    Posted in the Differential Equations Forum
    Replies: 5
    Last Post: October 7th 2009, 01:44 AM
  5. Replies: 2
    Last Post: September 7th 2009, 02:01 PM

Search Tags


/mathhelpforum @mathhelpforum