Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Linear Algebra and DE

  1. Apr 24, 2005 #1
    Say I have a nonhomogeneous ODE:
    y^(n) + ... + a1 y' + a0y = x

    Define the differential operator Dx = x',
    and p(D) = D^n + a_n-1 D^n-1 +...+a1 D + a0 I

    Let C be the set of functions that can be differentiated as many times as we want.

    Given Lemma: D - c I : C-->C is onto for c in complex.

    Prove for all x in C there exists a solution y in C.

    Is the following correct?

    Write p(D) = (D - c1 I)(D - c2 I)...(D - cn I)

    By the lemma, p(D) is onto.

    If p(D) is onto, then there exists a y in C such that p(D)x = y.
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted

Similar Discussions: Linear Algebra and DE
  1. Linear Algebra (Replies: 4)

  2. Linear Algebra (Replies: 1)

  3. Linear algebra (Replies: 2)

  4. Linear algebra (Replies: 2)