Results 1 to 3 of 3
Like Tree1Thanks
  • 1 Post By topsquark

Math Help - First order exact diff. equation.

  1. #1
    Junior Member BERMES39's Avatar
    Joined
    Aug 2011
    Posts
    41

    First order exact diff. equation.

    In this solution for an exact differential equation I can't reconcile my answer with the book's answer. Please help.
    Attached Thumbnails Attached Thumbnails First order  exact diff. equation.-diffeq-1.jpg  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,853
    Thanks
    321
    Awards
    1

    Re: First order exact diff. equation.

    I've never seen the solution method that you have presented so I can't find if there's an error in it. On the other hand if we look at the solution method I know I do not get your book answer either. The fix is trivial and I suspect a typo. I'll run through how I know how to do it and maybe you can compare the two methods to find where your problem is.

    I won't bother to prove that your original equation is exact. I'm assuming you already checked that. So I will start with the assumption that there is a function F(x, y) such that
     \frac{\partial F}{\partial x} = P(x, y) = e^x sin(y) + e^{-y}

    which means that
    F(x, y) = \int P(x, y) \partial x + \phi (y)
    (The \partial x in the integrand is merely to specify we are keeping the value of y fixed during the integration.)

    This leads to
    F(x, y) = e^x sin(y) + xe^{-y} + \phi (y)

    We also know that
    \frac{\partial F}{\partial y} = Q(x, y)

    Integrating this out we get that \phi (y) = C

    So the final solution will be
    F(x, y) = e^x sin(y) + xe^{-y} + C

    whereas the book claims F(x, y) = C = e^x sin(y) + xe^{-y}. Hence the suspicion of a typo.

    -Dan
    Last edited by topsquark; January 11th 2013 at 03:35 PM.
    Thanks from BERMES39
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member BERMES39's Avatar
    Joined
    Aug 2011
    Posts
    41

    Re: First order exact diff. equation.

    thank you, it makes sense.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. How to solve this second order Diff. Equation.
    Posted in the Differential Equations Forum
    Replies: 8
    Last Post: September 23rd 2011, 03:11 PM
  2. 2nd order diff equation!
    Posted in the Differential Equations Forum
    Replies: 8
    Last Post: October 30th 2010, 04:31 PM
  3. [SOLVED] 2nd order diff. equation
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: September 20th 2010, 01:11 PM
  4. 1st order homogeneous diff. equation
    Posted in the Differential Equations Forum
    Replies: 6
    Last Post: January 31st 2010, 10:36 AM
  5. 2nd Order homogeneous diff equation
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: January 28th 2010, 11:43 AM

Search Tags


/mathhelpforum @mathhelpforum