Results 1 to 3 of 3

Math Help - solve the differential equation by undetermined coefficients

  1. #1
    Senior Member
    Joined
    Aug 2009
    Posts
    349

    solve the differential equation by undetermined coefficients

    y'''-3y''+3y'-y=x-4e^x

    ok so i found the roots of the equation where m = 1 and then i got my yc equation which was also pretty straight forward.

    what i am having problems with is the yp equation,

    i made my guess to be: Ax + Bx^3e^x <--- my book said i was wrong?

    any help would be appreciated...
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Mar 2010
    From
    Florida
    Posts
    3,093
    Thanks
    5
    Quote Originally Posted by slapmaxwell1 View Post
    y'''-3y''+3y'-y=x-4e^x

    ok so i found the roots of the equation where m = 1 and then i got my yc equation which was also pretty straight forward.

    what i am having problems with is the yp equation,

    i made my guess to be: Ax + Bx^3e^x <--- my book said i was wrong?

    any help would be appreciated...
    I think it should be just Ax+Be^x
    Follow Math Help Forum on Facebook and Google+

  3. #3
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    5
    Awards
    2
    Quote Originally Posted by dwsmith View Post
    I think it should be just Ax+Be^x
    When you plug that into the LHS, the operator will annihilate the exponential, so there's no way you'll get the RHS out of that. Because the root m = 1 has multiplicity 3, your particular solution will have to look something like slapmaxwell1's candidate. I might recommend have something more like

    y_{p}=A+Bx+Ce^{x}+Dxe^{x}+Ex^{2}e^{x}+Fx^{3}e^{x}.

    That might be overkill, but it might not. A hunch: any of those constant that are superfluous will be easy to solve for, I think. So I don't think you'll waste too much time doing it this way.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Higher order differential equations, undetermined coefficients?
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: October 13th 2011, 04:06 PM
  2. solve the given differential by undetermined coefficients...
    Posted in the Differential Equations Forum
    Replies: 7
    Last Post: March 5th 2011, 07:36 PM
  3. Replies: 1
    Last Post: May 4th 2009, 08:21 PM
  4. Replies: 8
    Last Post: March 14th 2009, 07:29 PM
  5. Differential equations - undetermined coefficients
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: March 12th 2009, 10:21 AM

Search Tags


/mathhelpforum @mathhelpforum