Results 1 to 6 of 6

Math Help - single solution

  1. #1
    MHF Contributor
    Joined
    Nov 2008
    Posts
    1,401

    single solution

    check for the following if they have a single solution on (-1,1)
    A)
    y'=\sqrt{|y|}
    y(0)=0
    B)
    y'=|y|^{3}
    y(0)=0
    Follow Math Help Forum on Facebook and Google+

  2. #2
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    5
    Awards
    2
    In order to find a singular solution, it must be referenced to a family of solutions that you've already found. That is, a singular solution is a solution that can't be expressed as a member of a family of solutions. What is the family of solutions you've already found?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Nov 2008
    Posts
    1,401
    for A :
    dy/dx=\sqrt{|y|}
    \int \frac{dy}{\sqrt{|y|}}=\int dx
    i dont know how to deal with the absolute value
    ill just egnore it
    2y^{\frac{1}{2}}=x
    4y=x^2 +c

    by single solutioni didnt mean singluar solution which for 1/x x=0 is a singular point of solution

    i ment like in lenear algebra where we get a single solution from a row redused matrice
    Last edited by transgalactic; November 13th 2010 at 10:18 PM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    5
    Awards
    2
    My mistake. I see what you mean now.

    I think you're off by a factor of 2 in your solution. You should always plug your solution back into the DE to make sure it solves the DE. It's easy and it prevents mistakes. I also think that y = 0 is a perfectly good solution for both (A) and (B). Hence, I think both of them have multiple solutions. Indeed, the conditions of the standard existence theorem are not satisfied, so you're not guaranteed a unique solution.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Nov 2008
    Posts
    1,401
    you are correct i fixed the original post
    so y=0 is the single solution
    ?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    5
    Awards
    2
    I would say that y = 0 is a singular solution. You cannot get the solution y = 0 from any choice of C in the family of solutions 4y=x^2 +c.

    There is more than one solution to the IVP's for both (A) and (B).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Prove sinx+cosx=x has a single solution
    Posted in the Calculus Forum
    Replies: 7
    Last Post: January 15th 2011, 06:25 PM
  2. Solving 2D Poisson problem with single series solution.
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: April 6th 2010, 01:06 PM
  3. Single equation, single unknown. How to solve?
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: March 14th 2010, 01:37 PM
  4. single solution?
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: June 8th 2009, 11:28 AM
  5. One More Single Log
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: August 8th 2008, 07:49 AM

Search Tags


/mathhelpforum @mathhelpforum