Results 1 to 3 of 3

Math Help - Ordinary Differential Equations questions (No problems)

  1. #1
    Senior Member
    Joined
    Jul 2007
    Posts
    290

    Ordinary Differential Equations questions (No problems)

    Just had a few questions that are on my mind about knowing how to tell one form from the other. The forms that we have learned are

    1. Separable (Easiest)
    2. Linear
    3. Exact
    4. Bernoulli
    5. Homogeneous

    Questions:

    1. I know that Linear is of the form

    dy/dx + P(x)y = Q(x). Given that y is the dependent variable, for this to work Q(x) cannot have any y variable correct? IF Q(x) DID have a y variable to the nth power, then it would be Bernoulli right?

    2. For a D.E. to be considered Exact, it must first pass the test for exactness even though it is of the form P(x)dx + Q(x)dy = 0 correct?

    3. I'm having a hard time knowing initially which method will prove to be the fastest and most efficient given some random problem in the book. Any tips or tricks you guys can let me know about?

    So far that's all the questions I have. Any feedback is much appreciated.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by JonathanEyoon View Post
    1. I know that Linear is of the form

    dy/dx + P(x)y = Q(x). Given that y is the dependent variable, for this to work Q(x) cannot have any y variable correct?
    Right. When we write Q(x) it immediately means that Q is a function of variable x only - so there is no y term.
    IF Q(x) DID have a y variable to the nth power, then it would be Bernoulli right?
    I think you want to say if instead of Q(x) we had Q(x)y^n. Yes, in that case we have a Bernoulli equation which can be turned into a first-order linear differencial equation - as above.

    2. For a D.E. to be considered Exact, it must first pass the test for exactness even though it is of the form P(x)dx + Q(x)dy = 0 correct?
    It needs to have the form M(x,y) + N(x,y)y' = 0 and \frac{\partial M}{\partial y} = \frac{\partial N}{\partial x}.

    3. I'm having a hard time knowing initially which method will prove to be the fastest and most efficient given some random problem in the book. Any tips or tricks you guys can let me know about?
    The best thing to do is to learn how to recognize what kind of differencial equation it is. Once you recognized it then you know the method to use to solve it.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Jul 2007
    Posts
    290
    Appreciated~ and thanks for showing me a different way to see Bernoulli.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Ordinary Differential Equations
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: November 17th 2010, 05:41 AM
  2. Ordinary differential equations....
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: July 22nd 2009, 11:13 AM
  3. Ordinary Differential Equations problems
    Posted in the Differential Equations Forum
    Replies: 9
    Last Post: February 15th 2009, 05:39 PM
  4. Ordinary differential equations
    Posted in the Differential Equations Forum
    Replies: 5
    Last Post: January 16th 2009, 06:13 AM
  5. Ordinary Differential Equations
    Posted in the Calculus Forum
    Replies: 1
    Last Post: July 1st 2008, 08:34 AM

Search Tags


/mathhelpforum @mathhelpforum