Results 1 to 6 of 6

Math Help - Help with diff eqn

  1. #1
    Junior Member
    Joined
    Nov 2006
    Posts
    32

    Wink Help with diff eqn

    How can I proceed with this? solve the diff eqn: \left (2y^2 - 4x + 5 \right )dx = \left (4 - 2y + 4xy \right )dy

    \frac{dy}{dx} = \frac{2y^2 -4x + 5}{4 -2y + 4xy}

    Doesn't seem I can use quotient rule here.

    ..............?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Eater of Worlds
    galactus's Avatar
    Joined
    Jul 2006
    From
    Chaneysville, PA
    Posts
    3,001
    Thanks
    1
    Forgive me if I err along the line, but PH or someone will be along to correct me if I wonder.

    It's been awhile.

    Now, check to see if your DE is exact.

    (2y^{2}-4x+5)dx=M(x,y)

    (4-2y+4xy)dy=N(x,y)


    M_{y}=4y=N_{x}

    There exists a function f(x,y), such that:

    \frac{\partial{f}}{\partial{x}}=2y^{2}-4x+5

    \frac{\partial{f}}{\partial{y}}=4-2y+4xy


    From the 1st equation, after integrating:

    f(x,y)=2xy^{2}+5x-2x^{2}+g(y)

    Take the partial derivative with respect to y of the last expression and set the result equal to N(x,y):

    \frac{\partial{f}}{\partial{y}}=4xy+g'(y)=4-2y+4xy

    g'(y)=4-2y

    and g(y)=4y-y^{2}

    f(x,y)=2xy^{2}+5x-2x^{2}+4y-y^{2}

    Therefore, \frac{\partial{f}}{\partial{x}}=2y^{2}-4x+5

    \frac{\partial{f}}{\partial{y}}=4-2y+4xy

    So, f(x,y)=2xy^{2}+5x-2x^{2}+4y-y^{2}


    Check to make sure I didn't boo-boo.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    I do not think so.

    First it needs to have the form,
    M(x,y)+N(x,y)y'=0
    And in this case,
    \frac{\partial M}{\partial y}=4y
    \frac{\partial N}{\partial x}=-4y
    Thus, this is not an exact differencial equation.
    Also, I do not think it is possible to find an integrating factor.

    But what I think happened is that the poster wrote a wrong question. And really meant what you wrote.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Eater of Worlds
    galactus's Avatar
    Joined
    Jul 2006
    From
    Chaneysville, PA
    Posts
    3,001
    Thanks
    1
    I kinda thought, but figured I'd take a stab, in case.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Nov 2006
    Posts
    32

    Smile

    Thanks for your help. This is how I got the question, Solve diff eqn -

    \left (2y^2 - 4x + 5 \right )dx = \left (4 - 2y + 4xy \right )dy
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by ashura View Post
    Thanks for your help. This is how I got the question, Solve diff eqn -

    \left (2y^2 - 4x + 5 \right )dx = \left (4 - 2y + 4xy \right )dy
    As I said, this is not an exact differencial equation. You cannot even find an integrating factor that will transform this into an exact differencial equation. This is not a homogenous equation because the polynomials are not homogenous of the same degree.

    Maybe, there is something else that you need to do, but it certainly is not one of the standard techiniques.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Diff Eq. x' = t * cos(t)
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: April 2nd 2010, 05:16 PM
  2. Diff eq IVP
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: December 10th 2009, 01:05 PM
  3. diff eqn, sin(2x).
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: March 12th 2009, 09:30 AM
  4. diff eq help
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: January 25th 2009, 01:16 PM
  5. diff eq help
    Posted in the Calculus Forum
    Replies: 0
    Last Post: March 31st 2008, 03:41 PM

Search Tags


/mathhelpforum @mathhelpforum