Results 1 to 2 of 2

Thread: Need help with a Wronskian problem.

  1. #1
    Member
    Joined
    Nov 2009
    Posts
    79

    Need help with a Wronskian problem.

    If the Wronskian W of f and g is $\displaystyle 3e^{4t}$, and if $\displaystyle f(t
    )=e^{2t}$ find g(t).

    I know we get $\displaystyle e^{2t}g'(t)-2e^{2t}g(t)=3e^{4t}$ which becomes $\displaystyle g'(t)-2g(t)=3e^{2t}$.

    It is after this that I am getting messed up. I know you use the integrating factor method to solve this, but I am not coming up with the correct answer shown in my book which is $\displaystyle g(t)=3te^{2t}+ce^{2t}$ I know how to solve first order linear questions but apparently I'm doing something wrong. Can someone help please?


    EDIT: I don't need help with this anymore! I realized the mistake I was making
    Last edited by steph3824; Mar 5th 2010 at 10:12 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member Black's Avatar
    Joined
    Nov 2009
    Posts
    105
    Ok, so we have

    $\displaystyle g'(t)-2g(t)=3e^{2t}$.

    So int. factor: $\displaystyle e^{-2\int dt}=e^{-2t}.$ Multiply both sides of the equation by the int. factor to get

    $\displaystyle e^{-2t}g'(t)-2e^{-2t}g(t)=\frac{d}{dt}(e^{-2t}g(t))= 3.$

    Integrate both sides with respect to t to get

    $\displaystyle e^{-2t}g(t)=3t+c \Longrightarrow g(t)=3te^{2t}+ce^{2t}$.

    Edit: Oops! Didn't see your edit.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Wronskian
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: Jan 13th 2011, 05:02 PM
  2. Need help with Wronskian
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: Mar 6th 2010, 07:50 PM
  3. Wronskian Problem
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: Aug 1st 2009, 12:57 PM
  4. Wronskian
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Oct 9th 2008, 05:48 PM
  5. Wronskian
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: Mar 19th 2007, 05:45 PM

Search Tags


/mathhelpforum @mathhelpforum