1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Differential equation

  1. Mar 13, 2010 #1
    Hi i've been striving to find the solution of this differential equation, but can't find: Y''*Y^2=C c being a real number. Please give me a hand with it. Thanks in advance!!!
  2. jcsd
  3. Mar 13, 2010 #2


    User Avatar
    Science Advisor

    Differential equations like this, which do not contain the independent variable, are called autonomous equations. Try:

    http://en.wikipedia.org/wiki/Autonomous_system_(mathematics [Broken])
    Last edited by a moderator: May 4, 2017
  4. Mar 16, 2010 #3
    Thanks for the source. I'll make my best to solve it. But i would like to have a person to help me with it though. I barely can use the internet. I am in Haiti.

    Can u try helping me with it please!!!
  5. Mar 17, 2010 #4


    User Avatar
    Homework Helper
    Gold Member

    You can get your first integral fairly easily. For this type of d.e. where x does not appear, you can define p = Y'. Then

    [tex]Y'' = \frac{dp}{dx} = \frac{dp}{dY}.\frac{dY}{dx} = p\frac{dp}{dY}[/tex]

    so you have a first-order equation in the variables p and Y.

    You can integrate that but then you have to do a second integration. Except if you take the constant of integration zero you have a rather nasty square root I think, but it can be done; if you don't know how maybe someone will help if you come back with the first part.
  6. Mar 18, 2010 #5
    hi buddy,
    Thanks for your help. Actually, it's the very same method a man here has proposed to me. And i ended up having one equation where i have my Y on one side, and the variable x on the other.
    When i kept integrating it gives me something with logarithm and square root with Y. i wanted to find Y in respect of x, but what i find is X in respect of y. i don't know how to calculate it so i find Y in respect of x. It's so weird and difficult to me cause i don't know any method that can help.
    Later today i will post the result here so that you give me an idea. I don't have the papers with me now.

    Thanks again, i thought i would find another method for it. i really appreciate your help
  7. Mar 18, 2010 #6


    User Avatar
    Science Advisor

    It sounds like you're on the right track. After you get x in terms of y, you need to invert this relation to get y in terms of x. Post what you have so we can see.
  8. Mar 20, 2010 #7
    Here is the equation it gave me. I resolved it, i didn't expect to come to the internet so i didn't come with the papers, so is it right? [tex]\int\sqrt{\frac{y}{by-c}} dy = \int\sqrt{2} dx[/tex]. b and c are real numbers!
  9. Mar 20, 2010 #8


    User Avatar
    Homework Helper
    Gold Member

    I think so, at least I got the same result except I made a mistake you didn't. So on the right you have got x basically. (NB c is your given constant whereas b is an arbitrary constant.)

    As I said you have to do a second integration - it is not clear to me whether you have, but you mentioned weird results which make it sound that you have. If you come back with more it shall be revealed to you, unless you twigged it already, how they are not wierd as they may seem but quite to be expected and useful! :smile:
    Last edited: Mar 20, 2010
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Differential equation
  1. Differential equations (Replies: 1)

  2. Differential equation (Replies: 4)

  3. Differential Equation (Replies: 12)

  4. Differential Equations (Replies: 1)