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

About the solutions of ODE

  1. May 29, 2014 #1
    Given the following ODE:

    ##ay''(t) + by'(t) + cy(t) = 0##

    The following solution:

    ##y(t) = c_1 \exp(x_1 t) + c_2 \exp(x_2 t)##

    is more general than:

    ##y(t) = A \exp(\sigma t) \cos(\omega t - \varphi)##

    ? Why?
     
  2. jcsd
  3. May 29, 2014 #2

    AlephZero

    User Avatar
    Science Advisor
    Homework Helper

    The solutions are equivalent if ##x_1## and ##x_2## are complex conjugate numbers.

    They are not equivalent if ##x_1## and ##x_2## are unequal real numbers, unless you want to use a crazy interpretation of ##cos(\omega t - \varphi)## where ##\omega## and ##\varphi## are complex constants.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: About the solutions of ODE
  1. Solution to ODE (Replies: 5)

  2. Solution to ODE (Replies: 1)

  3. Solution of ODE (Replies: 4)

  4. The solution of ODE (Replies: 5)

Loading...