Results 1 to 3 of 3

Math Help - Solution of a simple Differential Equation

  1. #1
    Newbie
    Joined
    Mar 2008
    Posts
    2

    Solution of a simple Differential Equation

    Hi,

    I was wondering if anyone could help me solve or even know the type of the differential equation below

    d^2x/dt^2= k.dy/dt

    where k is a constant.


    Thanks very much

    Gareth
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,824
    Thanks
    318
    Awards
    1
    Quote Originally Posted by gabrown View Post
    Hi,

    I was wondering if anyone could help me solve or even know the type of the differential equation below

    d^2x/dt^2= k.dy/dt

    where k is a constant.


    Thanks very much

    Gareth
    \frac{d^2x}{dt^2} = k~\frac{dy}{dt}

    So
    \int \frac{d^2x}{dt^2}~dt = k \int \frac{dy}{dt}~dt

    \frac{dx}{dt} = ky + C

    This is as far as we can go unless you want to put the solution in integral form:
    \int \frac{dx}{dt}~dt = k \int y(t)~dt + Ct

    x(t) = k \int y(t)~dt + Ct + A

    -Dan
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Mar 2008
    Posts
    2
    Quote Originally Posted by topsquark View Post
    \frac{d^2x}{dt^2} = k~\frac{dy}{dt}

    So
    \int \frac{d^2x}{dt^2}~dt = k \int \frac{dy}{dt}~dt

    \frac{dx}{dt} = ky + C

    This is as far as we can go unless you want to put the solution in integral form:
    \int \frac{dx}{dt}~dt = k \int y(t)~dt + Ct

    x(t) = k \int y(t)~dt + Ct + A

    -Dan

    so if we have

    d^2y/dt^2= -k.dx/dt

    as well can we come up with a way of putting x and y as just functions of t?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. differential equation solution
    Posted in the Differential Equations Forum
    Replies: 4
    Last Post: September 29th 2010, 03:04 AM
  2. Differential equation solution
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: August 26th 2010, 06:47 AM
  3. Is this a solution to the differential equation?
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: May 21st 2010, 06:19 PM
  4. Particular Solution to Differential Equation!!!
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: May 29th 2009, 12:14 PM
  5. solution of a differential equation
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: November 7th 2008, 07:18 PM

Search Tags


/mathhelpforum @mathhelpforum