Results 1 to 3 of 3

Math Help - Differential Equation Problem

  1. #1
    Newbie
    Joined
    Jan 2008
    Posts
    16

    Differential Equation Problem

    (x+y) * (dy/dx) = (x-y)

    the given answer is y^2-2xy-x^2 = C

    The problem is in a section of the textbook where substitution methods are taught. That is, making a subsitution where v = some term containing the variables x and y. Then solving the substitution equation so that y = some term containing the variables x and v. Taking the derivative of that term so dy/dx can be substituted for. Then the next step would be to separate the variables x and v. integrate, and lastly you substutite x and y back in for v to gain your solution to the Diff EQN.

    Problem is, I can't do it.

    Help is much appreciated!

    JB
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    13
    Quote Originally Posted by jblorien View Post
    (x+y) * (dy/dx) = (x-y)

    the given answer is y^2-2xy-x^2 = C
    First rewrite your equation as follows:

    \frac{{dy}}<br />
{{dx}} = \frac{{x - y}}<br />
{{x + y}}.

    Now multiply top & bottom by \frac1x,

    \frac{{dy}}<br />
{{dx}} = \frac{{1 - \dfrac{y}<br />
{x}}}<br />
{{1 + \dfrac{y}<br />
{x}}}.

    Now it remains to substitute y=ux.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jan 2008
    Posts
    16
    Thank you
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: April 11th 2011, 01:17 AM
  2. Differential Equation Problem 2
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: September 28th 2009, 12:31 AM
  3. Differential equation problem
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: March 22nd 2009, 02:25 AM
  4. differential equation problem - help please!
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 24th 2008, 07:59 AM
  5. Differential Equation Problem
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 23rd 2007, 05:30 AM

Search Tags


/mathhelpforum @mathhelpforum