Results 1 to 4 of 4
Like Tree1Thanks
  • 1 Post By chiro

Math Help - Solving difficult differential equation

  1. #1
    Junior Member
    Joined
    Jun 2010
    Posts
    48

    Solving difficult differential equation

    I have the following differential equation which I want to solve for y as a function of x

    \frac{\partial y}{\partial x}=\frac{C_{1}\left(C_{5}y+C_{6}\right)^{2}}{C_{2}  \left(C_{3}y+C_{4}\right)-C_{7}\left(C_{5}y+C_{6}\right)^{6}}

    where C_{1},C_{2},C_{3},C_{4},C_{5},C_{6},C_{7} are constants.
    Can anyone suggest a method for solving this equation.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,664
    Thanks
    606

    Re: Solving difficult differential equation

    Hey JulieK.

    Since your expression is separable, you will need to integrate the inverse of the RHS with respect to y. You will have a ratio of two polynomials which means you will need to look at a variety of methods like partial fractions, substitutions, logarithm derivatives and so on.

    Have you got access to a table of integrals? If not do a google search and take a look.
    Thanks from topsquark
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jun 2010
    Posts
    48

    Re: Solving difficult differential equation

    Hi chiro

    Many thanksfor your reply.
    I know this can be integrated but this is not very useful for me.
    What I want is y as an explicit function of x. What the integration produces is x as a function of y.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,664
    Thanks
    606

    Re: Solving difficult differential equation

    That will depend on the answer you get. If you can't get y = f(x) then you will have to leave it at that.

    Also you can still evaluate y as a function of x using implicit differentiation and putting that through a numerical solver with enough accuracy to keep errors below some threshold: this is what is typically done if you have an implicit function (something that doesn't have y = f(x)).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Solving difficult equation
    Posted in the Calculus Forum
    Replies: 10
    Last Post: June 9th 2010, 03:19 AM
  2. finding general solution (difficult differential equation)
    Posted in the Differential Equations Forum
    Replies: 5
    Last Post: May 10th 2010, 10:22 PM
  3. Difficult Differential Equation System
    Posted in the Differential Equations Forum
    Replies: 0
    Last Post: August 8th 2009, 05:17 PM
  4. Solving a difficult equation
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: May 31st 2008, 08:43 PM
  5. Solving a difficult equation
    Posted in the Calculus Forum
    Replies: 7
    Last Post: April 7th 2008, 08:44 AM

Search Tags


/mathhelpforum @mathhelpforum