Results 1 to 2 of 2

Math Help - Simple DE....but lack of practice.

  1. #1
    Newbie
    Joined
    Aug 2009
    From
    Melbourne
    Posts
    11

    Simple DE....but lack of practice.

    Hey,
    I haven't looked at differential equations for some years... and I'm having trouble with two really simple ones....

    \frac{dx}{dt} = (x + 2),    x(0) = 1 ........ODE (1)

    and \frac{dy}{dt} = 2y,   y(0) = 1............ ODE (2)

    The text I'm looking at says the answers for ODE (1) and ODE (2) should be x + 2 = 3e^t and y = e^{2t} respectively.

    I thought the solutions (not imposing the initial conditions are) for each of the conditions are

    xt + 2t and 2yt respectively.

    I must be doing this incorrectly. Do I use separation of variables?

    \int \frac{dx}{x+2} = \int \ dt

    and

    \int \frac{dy}{y} = \int 2 dt ?

    If so, how do I integrate \int \frac{dx}{x+2} and \int \frac{dy}{y} ?

    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Dec 2009
    From
    1111
    Posts
    872
    Thanks
    3
    Quote Originally Posted by JavaJunkie View Post
    Hey,
    I haven't looked at differential equations for some years... and I'm having trouble with two really simple ones....

    \frac{dx}{dt} = (x + 2),    x(0) = 1 ........ODE (1)

    and \frac{dy}{dt} = 2y,   y(0) = 1............ ODE (2)

    The text I'm looking at says the answers for ODE (1) and ODE (2) should be x + 2 = 3e^t and y = e^{2t} respectively.

    I thought the solutions (not imposing the initial conditions are) for each of the conditions are

    xt + 2t and 2yt respectively.

    I must be doing this incorrectly. Do I use separation of variables?

    \int \frac{dx}{x+2} = \int \ dt

    and

    \int \frac{dy}{y} = \int 2 dt ?

    If so, how do I integrate \int \frac{dx}{x+2} and \int \frac{dy}{y} ?

    Thanks
    Dear JavaJunkie,

    Yes you should use seperation of variables. And remember that, \int{\frac{1}{x+c}}dx=\ln{\mid{x+c}\mid}~;~where~C  ~is~an~arbitary~constant. Hope you would be able to continue.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. UK maths postdocs (and lack thereof)
    Posted in the Math Forum
    Replies: 3
    Last Post: September 30th 2011, 04:45 AM
  2. lack of uniform convergence
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: September 1st 2011, 10:52 AM
  3. Replies: 14
    Last Post: February 27th 2010, 02:53 PM
  4. Lack-of-Fit Test
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: December 17th 2009, 10:49 PM

Search Tags


/mathhelpforum @mathhelpforum