Results 1 to 2 of 2

Math Help - Proof of Differential Equation Identities

  1. #1
    Newbie
    Joined
    Oct 2009
    Posts
    1

    Post Proof of Differential Equation Identities

    Hi guys I'm new here and I thought that maybe you could help me with this problem. I don't quite understand the notation and what the thing is meaning.

    Prove the following:

    (D-a)(D-b){f(x)e^(λx)} = e^(λx)(D+λ-a)(D+λ-b)f(x)
    (D^2+aD+b){f(x)e^(λx)} = e^(λx){(D+λ)^2+a(D+λ)+b}f(x)

    I just know that D=\frac {d}{dx}
    But what does the curly parenthesis notation mean?

    Any ideas?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Jester's Avatar
    Joined
    Dec 2008
    From
    Conway AR
    Posts
    2,367
    Thanks
    42
    Quote Originally Posted by Jiggy View Post
    Hi guys I'm new here and I thought that maybe you could help me with this problem. I don't quite understand the notation and what the thing is meaning.

    Prove the following:

    (D-a)(D-b){f(x)e^(λx)} = e^(λx)(D+λ-a)(D+λ-b)f(x)
    (D^2+aD+b){f(x)e^(λx)} = e^(λx){(D+λ)^2+a(D+λ)+b}f(x)

    I just know that D=\frac {d}{dx}
    But what does the curly parenthesis notation mean?

    Any ideas?
    Expand (the \{ \} are just brackets to group things together)

     <br />
(D-a) \left\{ e^{\lambda x} f(x)\right\} = D \left\{e^{\lambda x} f(x)\right\} - a e^{\lambda x} f(x)<br />

     <br />
= D \left(e^{\lambda x}\right)\cdot f(x) + e^{\lambda x} D f(x) - a e^{\lambda x} f(x)<br />

     <br />
= \lambda e^{\lambda x} \cdot f(x) + e^{\lambda x} D f(x) - a e^{\lambda x} f(x)<br />

    then factor

     <br />
= e^{\lambda x} \left( D f(x) + (\lambda - a) f(x) \right) <br />

     <br />
= e^{\lambda x} \left( D + \lambda - a \right) f(x).<br />

    The rest is similar.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: July 4th 2011, 02:39 AM
  2. Replies: 0
    Last Post: April 1st 2011, 08:36 AM
  3. Gompertz differential equation proof
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 8th 2010, 01:14 PM
  4. Vector differential identities
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 15th 2007, 02:36 PM
  5. Differential Equation Proof
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 30th 2006, 08:34 PM

Search Tags


/mathhelpforum @mathhelpforum