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    Bugbear in the Playground
     
    HalflingPirate

    Join Date
    Jan 2013
    Location
    Arkansas, U.S.
    Gender
    Male

    Default How in the world do I solve this differential equation?

    dy/dx = x(x-y)

    I've been staring at this for the past half hour, and I'm completely stumped. I can't separate the variables, but I can't integrate it in this form either. I don't know what to do.

    EDIT: I feel dumb now. This is dy/dx + P(x)y=Q(x).

    Am I correct in thinking that P(x) can = x?
    Last edited by MonkeySage; 2018-02-06 at 01:03 AM.

  2. - Top - End - #2
    Titan in the Playground
     
    Knaight's Avatar

    Join Date
    Aug 2008

    Default Re: How in the world do I solve this differential equation?

    Quote Originally Posted by MonkeySage View Post
    Am I correct in thinking that P(x) can = x?
    Is x a function of x?

  3. - Top - End - #3
    Ogre in the Playground
     
    Flumph

    Join Date
    Sep 2013

    Default Re: How in the world do I solve this differential equation?

    Quote Originally Posted by MonkeySage View Post
    dy/dx = x(x-y)

    I've been staring at this for the past half hour, and I'm completely stumped. I can't separate the variables, but I can't integrate it in this form either. I don't know what to do.

    EDIT: I feel dumb now. This is dy/dx + P(x)y=Q(x).

    Am I correct in thinking that P(x) can = x?
    My understanding is that you do this:

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

    for f(y), x and x^2 are constants.

    y = (x^2)y - (x/2)(y^2)

    If you want y in terms of x, then divide by y on both sides and then seperate the variables.

    1 = (x^2) - (x/2)y

    (x/2)y = (x^2)-1

    y = 2x - (2/x) or y = 2x - 2(x^-1)

    I could be in error though. It's been a while since I had to do this sort of maths.

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