Results 1 to 5 of 5

Math Help - how to find explicit solution

  1. #1
    Junior Member
    Joined
    Aug 2007
    Posts
    71

    how to find explicit solution

    (1) Consider the initial value problem
    dx/dt = -1/tx
    , x(−1) = 1
    (a) Use an analytic method to find an explicit solution for this
    problem. What is the domain of definition for this solution?

    What does it mean to "use an analytic method"?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,564
    Thanks
    1425
    Quote Originally Posted by lord12 View Post
    (1) Consider the initial value problem
    dx/dt = -1/tx
    , x(−1) = 1
    (a) Use an analytic method to find an explicit solution for this
    problem. What is the domain of definition for this solution?

    What does it mean to "use an analytic method"?
    This is a separable DE

    \frac{dx}{dt} = -\frac{1}{tx}

    x\,\frac{dx}{dt} = -\frac{1}{t}

    \int{x\,\frac{dx}{dt}\,dt} = \int{-\frac{1}{t}\,dt}

    \int{x\,dx} = -\ln{|t|} + C_1

    \frac{1}{2}x^2 + C_2 = -\ln{|t|} + C_1

    \frac{1}{2}x^2 = -\ln{|t|} + C_1 - C_2

    x^2 = -2\ln{|t|} + 2C_1 - 2C_2

    x^2 = -2\ln{|t|} + C, where C = 2C_1 - 2C_2

    x = \sqrt{C - 2\ln |t|}


    Now use the initial condition to find C.
    Last edited by mr fantastic; September 20th 2009 at 03:17 PM. Reason: Added close tag on last line of latex
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Aug 2007
    Posts
    71
    but ln(-1) is undefined!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by lord12 View Post
    but ln(-1) is undefined!
    No. It isn't. (For real numbers, anyway).

    Luckily however, the solution you were given does not lead to this number .... (In other words, read the given answer more carefully).
    Last edited by mr fantastic; September 20th 2009 at 07:43 PM. Reason: Saying "Yes. It is" (ie. agreeing with what the OP said) might be confused with "Yes. It is defined" (which I'm NOT saying).
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,564
    Thanks
    1425
    Quote Originally Posted by lord12 View Post
    but ln(-1) is undefined!
    Does the answer ask you to find \ln{(-1)}?

    No.

    It asks you to find \ln{|-1|} = \ln{1} = 0.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: November 25th 2010, 04:11 AM
  2. Replies: 2
    Last Post: September 7th 2009, 02:01 PM
  3. Replies: 1
    Last Post: August 4th 2009, 06:36 AM
  4. Find an explicit particular solution
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: July 11th 2009, 12:32 PM
  5. find the explicit formula for sequence
    Posted in the Algebra Forum
    Replies: 1
    Last Post: September 26th 2008, 04:24 PM

Search Tags


/mathhelpforum @mathhelpforum