Page 1 of 2 12 LastLast
Results 1 to 15 of 16

Math Help - Differential Equations?

  1. #1
    Newbie
    Joined
    Oct 2012
    From
    United States
    Posts
    9

    Differential Equations?

    Hi, I was wondering if anyone could help me with this problem. The differential equation y'=4y/x has a power function solution y=Ax^n if y(3)=162, determine the values of n and A. Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: Differential Equations?

    The ODE is separable...can you write it in this form?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2012
    From
    United States
    Posts
    9

    Re: Differential Equations?

    i can honestly say, i don't know what you're talking about haha i'm sorry i just started calc a month ago...
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: Differential Equations?

    I'm sorry, ODE is short for ordinary differential equation. I assumed you were beginning a course in ordinary differential equations.

    When you separate the variables, you typically get everything involving the dependent variable on the left and the independent variable on the right. For this ODE, you would then have:

    \frac{1}{y}\.dy=\frac{4}{x}\,dx

    Now, integrate...what do you get?
    Last edited by MarkFL; October 21st 2012 at 10:58 PM.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Oct 2012
    From
    United States
    Posts
    9

    Re: Differential Equations?

    I'm still a little confused with all this new terminology but are you saying that on the left it would be 1/y (162) = 4/x (3)...I might be completely wrong...sorry
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: Differential Equations?

    When you integrate, you will have:

    \int\frac{1}{y}\,dy=4\int\frac{1}{x}\,dx

    I am assuming you have been taught \int\frac{1}{u}\,du=\ln|u|+C. You need only write the constant of integration on one side, and it is typically written on the right side with the independent variable. It can be thought of as the composite constant from both integrations.

    See if you can write the next step, and from there we will use the properties of logs to get the desired form.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Oct 2012
    From
    United States
    Posts
    9

    Re: Differential Equations?

    I have not been taught that form before. is that the only way to attack this problem? because i feel a little lost at the moment.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: Differential Equations?

    Hmm...if you have not seen that rule of integration, then perhaps you are to just take the given solution:

    (1) y=Ax^n

    and then differentiate it with respect to x and write the resulting differential equation in the given form. Using this and the point on the solution curve (3,162), you will then have two equations and two unknowns from which you can determine A and n.

    What do you get when you differentiate (1) with respect to x?

    I apologize for the confusion, I assumed you were to solve the ODE and show that the solution is of the given form.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Newbie
    Joined
    Oct 2012
    From
    United States
    Posts
    9

    Re: Differential Equations?

    Without any numbers plugged in, i assume it would be y= Anx^n-1 but if you put in (3,162), would it be, 162=A(3n)^n-1
    Follow Math Help Forum on Facebook and Google+

  10. #10
    MHF Contributor Siron's Avatar
    Joined
    Jul 2011
    From
    Norway
    Posts
    1,250
    Thanks
    20

    Re: Differential Equations?

    First, compute the derivative
     y = Ax^{n} \Rightarrow y' = Anx^{n-1}
    Substitute y and y' in the differential equation:
    Anx^{n-1} =  \frac{4Ax^n}{x}
    \Leftrightarrow n=4

    At this point we can use that y(3)=162 thus
    y(3)=162 = 81A \Leftrightarrow A = 2

    Therefore the solution is:
    y=2x^4
    Follow Math Help Forum on Facebook and Google+

  11. #11
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: Differential Equations?

    I guess I was taking too long! LOL!
    Follow Math Help Forum on Facebook and Google+

  12. #12
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,842
    Thanks
    320
    Awards
    1

    Re: Differential Equations?

    @ chyksparks333

    Since you have decided to not allow PMs we have to do this in public. You reported this post and said that there was something in the thread that was "not cool." I have reviewed the thread and I don't see what you could be reacting to. Please let me know as soon as you can.

    -Dan
    Follow Math Help Forum on Facebook and Google+

  13. #13
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: Differential Equations?

    I hope it wasn't my previous comment...I was only trying to be funny.
    Follow Math Help Forum on Facebook and Google+

  14. #14
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,842
    Thanks
    320
    Awards
    1

    Re: Differential Equations?

    Quote Originally Posted by MarkFL2 View Post
    I hope it wasn't my previous comment...I was only trying to be funny.
    I wouldn't worry. If they haven't responded by now it isn't important to them.

    -Dan
    Follow Math Help Forum on Facebook and Google+

  15. #15
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,367
    Thanks
    1312

    Re: Differential Equations?

    I'm a bit late on this but note that the problem does NOT ask you to solve the equation. You are given that the solutions is y= Ax^n for some A and n and you are asked to find A and n. Siron's method- find the derivative of y, then put that and y into the equation, is the correct idea.
    Follow Math Help Forum on Facebook and Google+

Page 1 of 2 12 LastLast

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: May 7th 2011, 10:26 AM
  2. 'Differential' in differential equations
    Posted in the Differential Equations Forum
    Replies: 0
    Last Post: October 5th 2010, 10:20 AM
  3. Replies: 2
    Last Post: May 18th 2009, 03:49 AM
  4. Replies: 5
    Last Post: July 16th 2007, 04:55 AM
  5. Replies: 3
    Last Post: July 9th 2007, 05:30 PM

Search Tags


/mathhelpforum @mathhelpforum