Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

henpen

  • 3 years ago

Mathematically, prove that there are there no arbitrary constants required for the particular solution of \[Ly=f(x)\].

  • This Question is Closed
  1. UnkleRhaukus
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    what is \(L\) ?

  2. henpen
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Linear DE operated on...

  3. henpen
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I know that it's obvious, but I've yet to encounter a formal proof.

  4. UnkleRhaukus
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i can not see the differential equation

  5. henpen
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Oh, it's just the general sign for\[Ly=\sum_{i=0}^{i=n}a_i\frac{d^i}{dx^i}y=0\]

  6. henpen
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Or is this only provable for more specific DE?

  7. UnkleRhaukus
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i thought there were usually as many constants in the solution as the order of the DE

  8. henpen
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Yes, but they're all in the complimentary solution.

  9. henpen
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I've not come across 'roots' with regards to DE, but I suppose so, yes.

  10. UnkleRhaukus
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    actually the roots are in the complementary solution

  11. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy