A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

Second order differential equations: 100(y'')-20(y)+y=0. Find general solution. Please explain how to obtain the general solution.

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

    PLEASE EXPLAIN STEPWISE!!

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

    isnt it 100 y'' -20 y' + y = 0

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

    oops yes

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

    ok you want a characteristic equation 100 r^2 - 20r + 1 = 0

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

    then?

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

    you have a double root, r = 1/10

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

    ya...then?

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

    If tex2html_wrap_inline96 (which happens if tex2html_wrap_inline98 ), then the general solution is displaymath64

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

    http://www.sosmath.com/diffeq/second/constantcof/constantcof.html

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

    the general solution is y = c1 *e^(1/10 x) + c2 *x *e^(1/10 x)

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

    is there a way to obtain without memorizing the formula?

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

    not that i know of

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

    there are 3 cases, distinct roots, double roots, and the imaginary roots. its not too bad, there is pattern

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

    the imaginary case is a little tricky

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

    thank you

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

    Can this method also solve differential equations of the form y"=f(x)?

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

    how will u proceed after u take y''=f(x)?

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

    yes it usually makes it easier to reduce the quadratic, except in the case where there are radical linear factors

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

    show that the defferential equation y(y^2+2x)+2x(y^2+x)dy/dx=0 is not exact, but that it has an integrating factor of the form u=x^2y^k for some integer k. hence or otherwise find the general solution of this differential equation

  20. 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

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.