1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

What happens if you only get 1 solution to a 2nd Order Diff EQ?

  1. Feb 17, 2006 #1
    Hello everyone, i'm slightly confused on this problem, when i factored it and solved for r, i came out with only 1 answer, r = -13/72
    Here is my problem and work:
    [​IMG]

    :biggrin:
     
  2. jcsd
  3. Feb 17, 2006 #2

    benorin

    User Avatar
    Homework Helper

    If you get repeated roots in your auxilary equation, e.g.

    [tex]y^{\prime\prime}-2y^{\prime}+1=0[/tex]

    has the auxilary equation

    [tex]r^{2}-2r+1=0[/tex] so [tex](r-1)^2=0[/tex]

    and hence r=1 (with multiplicity 2) so the general solution is of the form

    [tex]y=Ae^t+Bte^t[/tex]

    The roots of the equation

    [tex]5184r^2+1827r+169=0[/tex]

    are [tex]r=-\frac{13}{72}[/tex] (with multiplicity 2) so your general solution is of the form...
     
    Last edited: Feb 17, 2006
  4. Feb 17, 2006 #3

    Tide

    User Avatar
    Science Advisor
    Homework Helper

    One way to see why the method proposed by Benorin is valid would be to write your solution as

    [tex]y = A e^{r_1 t} + B e^{r_2 t}[/tex]


    and apply the initial conditions to determine the coefficients. Then let [itex]r_2[/itex] approach [itex]r_1 = r[/itex] (the root of your actual equation). Usually, l'Hopital's Rule can be applied to yield Benorin's solution.
     
  5. Feb 18, 2006 #4
    Thanks guys, i don't know if its right or not, but i think my method is right:
    [​IMG]
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: What happens if you only get 1 solution to a 2nd Order Diff EQ?
  1. 2nd order diff Eq help! (Replies: 14)

  2. 2nd order diff eq. (Replies: 1)

Loading...