Results 1 to 2 of 2

Math Help - [SOLVED] differential equation

  1. #1
    Super Member malaygoel's Avatar
    Joined
    May 2006
    From
    India
    Posts
    648

    [SOLVED] differential equation

    Solve
     (x^2 + y^2 + x)dx=-xydy


    Keep Smiling
    Malay
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by malaygoel View Post
    Solve
     (x^2 + y^2 + x)dx=-xydy


    Keep Smiling
    Malay
    recall that exact differential equations are those of the form M(x,y)~dx + N(x,y)~dy = 0, where \frac {\partial M}{\partial y} = M_y = N_x = \frac {\partial N}{\partial x}

    So this guy starts off looking like an exact equation, right, with M(x,y) = x^2 + y^2 + x and N(x,y) = xy

    but lo and behold, M_y = 2y \ne N_x = y. thus we need to find an integrating factor

    Recall that we can find the integrating factor \mu by the differential equation:

    \frac {d \mu}{dx} = \frac {M_y - N_x}{N} \mu

    so here we have:

    \frac {d \mu}{dx} = \frac {2y - y}{xy} \mu = \frac {\mu}{x}

    \Rightarrow \mu (x) = x

    multiplying through by x we obtain:

    \left( x^3 + xy^2 + x^2 \right)~dx + \left( x^2y \right)~dy = 0

    which is now an exact equation, since M_y = 2xy = N_x

    can you continue?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Differential equation
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: November 5th 2009, 05:44 AM
  2. [SOLVED] Differential equation
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: October 28th 2009, 06:16 PM
  3. [SOLVED] Differential Equation
    Posted in the Differential Equations Forum
    Replies: 4
    Last Post: January 25th 2009, 05:33 PM
  4. [SOLVED] Differential Equation Help
    Posted in the Differential Equations Forum
    Replies: 6
    Last Post: September 20th 2008, 07:48 PM
  5. [SOLVED] Differential Equation
    Posted in the Differential Equations Forum
    Replies: 0
    Last Post: September 14th 2008, 12:19 PM

Search Tags


/mathhelpforum @mathhelpforum