Results 1 to 3 of 3

Math Help - Method of Undetermined Coefficients

  1. #1
    Member
    Joined
    Jan 2008
    Posts
    175

    Method of Undetermined Coefficients

    y"+9y = t^2(e^{3t}) + 6


    ok wow, I have racked my brain at on this for about 5 hours with and without a study group.

    I cannot seem how to set up the initial part of finding the particular solution.

    I had found one variable and one point which was c = 1/162 but couldnt find A, or B.

    I tried using y(t)=(e^{3t})(at^{2} + bt +c) but got stock when plugging in the second derivative in and couldnt not find answer for the rest of the coefficients.

    what am I doing wrong?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,685
    Thanks
    616
    Hello, p00ndawg!

    y"+9y \:=\: t^2e^{3t} + 6

    I cannot seem how to set up the initial part of finding the particular solution.

    I tried: . y(t)\:=\:e^{3t}\left(At^2 + Bt +C\right) but got stuck.
    We need something to create the final "6".

    I tried: . y \:=\:At^2e^{3t} + Bte^{3t} + Ce^{3t} + D

    And came up with: . A = \frac{1}{18},\;B = -\frac{1}{27},\;C = \frac{1}{162},\;D = \frac{2}{3}

    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Jan 2008
    Posts
    175
    Quote Originally Posted by Soroban View Post
    Hello, p00ndawg!

    We need something to create the final "6".

    I tried: . y \:=\:At^2e^{3t} + Bte^{3t} + Ce^{3t} + D

    And came up with: . A = \frac{1}{18},\;B = -\frac{1}{27},\;C = \frac{1}{162},\;D = \frac{2}{3}


    wait im not understanding, what did you do?

    that is right tho, because b should equal -6 when you factor out the 162.

    what i did was right? or wrong?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Method of undetermined coefficients
    Posted in the Differential Equations Forum
    Replies: 5
    Last Post: November 29th 2011, 03:59 PM
  2. Method of Undetermined Coefficients
    Posted in the Differential Equations Forum
    Replies: 8
    Last Post: May 5th 2010, 04:13 AM
  3. Method of Undetermined coefficients
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: October 23rd 2009, 06:05 PM
  4. Method of Undetermined Coefficients
    Posted in the Calculus Forum
    Replies: 5
    Last Post: November 14th 2008, 02:15 AM
  5. Method of Undetermined Coefficients
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 15th 2008, 02:48 PM

Search Tags


/mathhelpforum @mathhelpforum