Results 1 to 3 of 3

Math Help - Unsure about this diff. equation......

  1. #1
    Newbie
    Joined
    Apr 2010
    Posts
    11

    Unsure about this diff. equation......

    Hi. Im a bit stuck on the following question: 'Find the general solutions of....


    x^2 (dy/dx) = y^2 (dx/dy)

    So Ive rearranged it as usual and seperated the variables to get:

    y^-2 (dy)^2 = x^-2 (dx)^2

    If dy and dx were not squared, I would know what to do. But what do I do now that theyre squared?


    Thanks in advance.

    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Jester's Avatar
    Joined
    Dec 2008
    From
    Conway AR
    Posts
    2,367
    Thanks
    42
    Quote Originally Posted by Croc View Post
    Hi. Im a bit stuck on the following question: 'Find the general solutions of....


    x^2 (dy/dx) = y^2 (dx/dy)

    So Ive rearranged it as usual and seperated the variables to get:

    y^-2 (dy)^2 = x^-2 (dx)^2

    If dy and dx were not squared, I would know what to do. But what do I do now that theyre squared?


    Thanks in advance.

    Take the square root of both sides.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor chisigma's Avatar
    Joined
    Mar 2009
    From
    near Piacenza (Italy)
    Posts
    2,162
    Thanks
    5
    The DE can be written as...

    \frac{dy}{dx} = \frac{y^{2}}{x^{2}}\cdot \frac{dx}{dy} (1)

    ... and if we multiply both terms of (1) by \frac{dy}{dx} we obtain...

    y^{' 2} = \frac{y^{2}}{x^{2}} (2)

    ... or equivalently...

    y^{'} = \pm \frac{y}{x} (3)

    The (3) is a complex of two first order DE and the solution of each of them is confortable enough...

    Kind regards

    \chi \sigma
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Diff. Equation
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: July 28th 2010, 10:18 AM
  2. Unsure how to solve exponential equation
    Posted in the Algebra Forum
    Replies: 3
    Last Post: August 25th 2009, 08:07 PM
  3. solving diff equation w/ bournoulli's equation
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 14th 2008, 06:06 PM
  4. Diff equation please
    Posted in the Calculus Forum
    Replies: 2
    Last Post: August 26th 2006, 04:49 PM
  5. Diff Equation
    Posted in the Calculus Forum
    Replies: 14
    Last Post: May 9th 2006, 07:10 AM

Search Tags


/mathhelpforum @mathhelpforum