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: Urnt? easy integration factor D.E. but its != correct, ahh!

  1. Jan 22, 2006 #1
    ello ello!
    Here is the problem:
    Let g(t) be the solution of the initial value problem:
    http://cwcsrv11.cwc.psu.edu/webwork2_files/tmp/equations/da/9fc0e62bc2df5df4721f38c5634c1f1.png [Broken]
    with g(1) = 1 .
    Find g(t).
    g(t) = ?

    Heres what i did:
    2ty' + y = 0;
    y' + y/(2t) = 0;

    I(t) = e^(2t) dt
    I = t^2;

    t^2*y = C;
    y = C/t^2;

    apply intial condition: g(1) = 1;
    1 = C/1
    C = 1;
    Appply constant:
    y = 1/t^2;
    which si wrong! :surprised

    Anyone know what I did?
    Last edited by a moderator: May 2, 2017
  2. jcsd
  3. Jan 22, 2006 #2
    I can't figure out what you did, but the equation is seperable so you dont need an integrating factor.
  4. Jan 22, 2006 #3


    User Avatar
    Science Advisor

    NO, the coefficient of y is [itex]\frac{1}{2t}[/itex] not 2t:
    [tex] I(t)= \int e^{\frac{1}{2t}}dt[/tex]
    [tex] \int e^{2t}dt[/itex]

    I think you will find that impossible to integrate so do this as a separable equation.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook