Results 1 to 2 of 2

Math Help - Operators

  1. #1
    Newbie
    Joined
    Dec 2010
    Posts
    3

    Operators

    Hello I really need help in understanding operators: the best way would be to show me how to solve:
    y''-y'-2y=e^(x)
    Thank you!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by deltafee View Post
    Hello I really need help in understanding operators: the best way would be to show me how to solve:


    Thank you!
    What exactly do you need to know. It can be rewritten as

    D^2y-Dy-2y=e^{x} This can be factored as

    (D^2-D-2)y=e^{x} \iff (D-2)(D+1)y=e^{x}

    So the homogeneous system (D-2)(D+1)y=0 has solutions

    e^{2x} because (D-2)e^{2x}=0 and

    e^{-x} because (D+1)e^{-x}=0

    So it has the complimentary solution y_c=c_1e^{2x}+c_2e^{-x}

    Now we can solve the original

    (D-2)(D+1)y=e^{x} by annihilating the right hand side with (D-1) since (D-1)e^{x}=0


    (D-1)(D-2)(D+1)y=(D-1)e^{x} \iff <br />
(D-1)(D-2)(D+1)y=0 since that factor is not repeated the particular solution has the form

    y_p=Ae^{x}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. binary operators
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: January 10th 2012, 02:56 AM
  2. [SOLVED] Linear Operators
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: December 27th 2010, 04:52 PM
  3. Hermitian operators
    Posted in the Advanced Algebra Forum
    Replies: 7
    Last Post: December 17th 2010, 02:54 AM
  4. Backshift operators
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: December 13th 2010, 10:38 PM
  5. Example of operators
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: October 10th 2010, 11:32 AM

Search Tags


/mathhelpforum @mathhelpforum