Simple ODE

Discussion in 'Math' started by boks, Nov 28, 2008.

  1. boks

    Thread Starter Active Member

    Oct 10, 2008
    218
    0
    y'(t) - ay(t) = 0

    What is the form of the solution? C \cdot e^{at}

    ?


    I have this ODE:

     T'(t) - (1 - \frac{n^2}{4})T(t) = 0

    If I'm right, the solutions should be of the form

    C \cdot e^{(1- \frac{n^2}{4})t}

    My book, however, says


    C \cdot e^ {1- \frac{n^2}{4}t}

    Who's right?
     
  2. blazedaces

    Active Member

    Jul 24, 2008
    130
    0
    Assuming that n is a constant, you're correct. Your book probably forgot to indicate the proper notation is all. I wouldn't rely too heavily on your books. Your books make mistakes too. Trust yourself sometimes too...

    -blazed
     
  3. boks

    Thread Starter Active Member

    Oct 10, 2008
    218
    0
    Brilliant.

    And how about the equation

    y' = (y - x)^2

    what's the form of the solution here?

    I find it hard to determine the form of solution of differential equations.
     
  4. blazedaces

    Active Member

    Jul 24, 2008
    130
    0
    You need to use substitution, look HERE.

    Good luck,
    -blazed
     
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