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Simple First Order ODE

  1. Nov 28, 2008 #1
    y'(t) - ay(t) = 0

    What is the form of the solution? [tex]C \cdot e^{at}[/tex]

    ?


    I have this ODE:

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

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

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

    My book, however, says


    [tex]C \cdot e^ {1- \frac{n^2}{4}t}[/tex]

    Who's right?
     
    Last edited: Nov 28, 2008
  2. jcsd
  3. Nov 28, 2008 #2

    Office_Shredder

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    I think the book forgot some parentheses
     
  4. Nov 28, 2008 #3
    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.
     
    Last edited: Nov 28, 2008
  5. Nov 28, 2008 #4

    Dick

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    I would try a simple substitution first. How about v=y-x? Now see if you can separate it in those variables.
     
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