Results 1 to 2 of 2

Math Help - [SOLVED] Swapping your dependent/independent variables? (ODE)

  1. #1
    Friedeggs123
    Guest

    [SOLVED] Swapping your dependent/independent variables? (ODE)

    I just discovered this board and it seems like an awesome idea. I have a question that I've been wracking my brains on for a while now and I can't find any answers from any other online sources so I was hoping that asking real people would help =).

    I have a question set that goes like this:

    Solve the following equations by regarding y as the independent variable rather than x

    and an example of one of the questions is:

    (1-4xy^2)dy/dx = y^3.

    Now, how do you swap the dependent/independent variables?

    Is the differential equation the same as

    (1-4xy^2) = y^3(dx/dy)?

    i.e., is dy/dx*dx/dy = 1?

    Thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by Friedeggs123 View Post
    I just discovered this board and it seems like an awesome idea. I have a question that I've been wracking my brains on for a while now and I can't find any answers from any other online sources so I was hoping that asking real people would help =).

    I have a question set that goes like this:

    Solve the following equations by regarding y as the independent variable rather than x

    and an example of one of the questions is:

    (1-4xy^2)dy/dx = y^3.

    Now, how do you swap the dependent/independent variables?

    Is the differential equation the same as

    (1-4xy^2) = y^3(dx/dy)? Mr F says: Yes.

    i.e., is dy/dx*dx/dy = 1?

    Thanks.
    So after some further re-arranging you have


    \frac{dx}{dy} +\frac{4}{y} x = \frac{1}{y^3}.


    Now use the integrating factor method to solve for x = x(y).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Graphing 2 independent and 1 dependent
    Posted in the Algebra Forum
    Replies: 2
    Last Post: December 12th 2011, 04:53 PM
  2. Replies: 0
    Last Post: November 14th 2011, 02:22 AM
  3. Independent or Dependent Events?
    Posted in the Algebra Forum
    Replies: 1
    Last Post: September 28th 2010, 06:20 PM
  4. Replies: 0
    Last Post: May 2nd 2010, 08:16 AM
  5. Independent or dependent
    Posted in the Statistics Forum
    Replies: 1
    Last Post: March 10th 2010, 11:31 AM

Search Tags


/mathhelpforum @mathhelpforum