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Homework Help: What did I do incorrectly?

  1. Oct 22, 2009 #1
    For #3, when going from the v(t) to y(t), I wasn't sure what to do with the
    C. When you get to the y(t), the last term is C / t^2. When you put in the
    initial condition y(0), you get an indeterminate expression C / 0.

    http://i111.photobucket.com/albums/n149/camarolt4z28/3.jpg [Broken]
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Oct 23, 2009 #2
    There isn't much you can do. However, C/0 is not indeterminate! It's simply undefined. "Indeterminate" only has meaning when the expression is inside the argument of a limit.
    Last edited by a moderator: May 4, 2017
  4. Oct 23, 2009 #3


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    You have y'= a(t)y+ f(t) and assert that the integrating factor is
    [tex]e^{\int a(t)dt}[/itex]
    That is incorrect. The formula is for a d.e. of the form y'+ a(t)y= f(t) so you have the sign wrong. The equation y'= -(2/t)y+ t-1 is equivalent to y'+ (2/t)y= t- 1. The integrating factor is
    [tex]e^{\int 2/t dt}= e^{2 ln|t|}= t^2[/tex].

    Of course, you are still going to have a problem at t= 0 because one of the coefficients of your d.e. is not defined at t= 0.
  5. Oct 23, 2009 #4
    Hm. I thought it didn't have to be in standard form.

    How do you get around the undetermined expression?
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