Results 1 to 5 of 5

Math Help - Help with a Differential Equation

  1. #1
    Newbie
    Joined
    Aug 2008
    Posts
    21

    Help with a Differential Equation

    How to go about solving this differential equation? I tried substitution and could not get any meaningful form of it.

    x + y + 1 + (−x + y − 3)y' = 0
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Jester's Avatar
    Joined
    Dec 2008
    From
    Conway AR
    Posts
    2,392
    Thanks
    56
    Quote Originally Posted by boredaxel View Post
    How to go about solving this differential equation? I tried substitution and could not get any meaningful form of it.

    x + y + 1 + (−x + y − 3)y' = 0
    Here you want to intoduce new variables x = u + a,\;\;\;y = v + b

    such that your new equation becomes

     u + v + ( -u + v) v' = 0 (homogeneous).

    So find a\;\;\text{and}\;\;b that makes this work.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Aug 2008
    Posts
    21
    Pardon me but I still cant see how I can solve the homogeneous DE. I cant find a way to separate the variables u and v.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by boredaxel View Post
    Pardon me but I still cant see how I can solve the homogeneous DE. I cant find a way to separate the variables u and v.
    You were told the type of DE it is .... To make it more explicit, your DE can be written as:

    \frac{dv}{du} = \frac{u + v}{u - v} = \frac{1 + \frac{v}{u}}{1 - \frac{v}{u}}.

    It should be clear what to do now. A similar problem is here: http://www.mathhelpforum.com/math-he...eneous-de.html
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Aug 2008
    Posts
    21
    !! Thanks for all the help. I understand what to do now.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Partial Differential Equation satisfy corresponding equation
    Posted in the Differential Equations Forum
    Replies: 0
    Last Post: May 16th 2011, 08:15 PM
  2. Replies: 4
    Last Post: May 8th 2011, 01:27 PM
  3. Replies: 1
    Last Post: April 11th 2011, 02:17 AM
  4. Partial differential equation-wave equation(2)
    Posted in the Differential Equations Forum
    Replies: 4
    Last Post: September 6th 2009, 09:54 AM
  5. Partial differential equation-wave equation - dimensional analysis
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: August 28th 2009, 12:39 PM

Search Tags


/mathhelpforum @mathhelpforum