1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Diff EQ - Simple Linear ODE

  1. Sep 26, 2006 #1

    So I solved this one linear DE and the answer I got isn't the same as the one in the back of my textbook... And I'm not sure why. I thought I was doing this right. Could someone tell me what I'm doing wrong?

    Here's what I'm given:

    [tex]integrating-factor\rightarrow e^{\int p(x) dx}=e^{\int \frac{1}{x}dx}= e^{lnx}=x[/tex]
    [tex]xy=\int x^{-2}dx=\frac{-1}{x}+C[/tex]

    That's what I get.

    The answer in the textbook is:

    Which is similar but not the same... What'd I do wrong?
  2. jcsd
  3. Sep 26, 2006 #2
    When you get an integrating factor, multiply it through both sides to obtain

    [tex] (xy)' = \frac{1}{x} [/tex]
    Then, Integrate to obtain
    [tex] \int d(xy) = \int \frac{1}{x} dx [/tex]
    And this leads you to
    [tex] y = \frac{ln(x)}{x} + Cx^{-1} [/tex]

    The step where you made the error was after the integrating factor, you did not also apply it to the right side of the equation, the [tex] x^{-2} [/tex].
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook