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!

Differential Equations [Show every member is a solution]

  1. Sep 8, 2009 #1
    problem resolved
     
    Last edited: Sep 8, 2009
  2. jcsd
  3. Sep 8, 2009 #2

    Mark44

    User Avatar
    Insights Author

    Staff: Mentor

    You should have gotten two specific values for r1 and r2, one of which happens to be a fraction. Show that the function y = aer_1 x + ber_2 x is a solution to your differential equation. That's it.
     
  4. Sep 8, 2009 #3
    I did get 2 answers, r= -1 and r=1/2. So now just plug those into the equation in part b ?
     
  5. Sep 8, 2009 #4

    Mark44

    User Avatar
    Insights Author

    Staff: Mentor

    Yes. Then for that function, show that 2y'' + y' - y = 0.
     
  6. Sep 8, 2009 #5

    O, okay thank you , it was really confusing me :confused:
     
  7. Sep 8, 2009 #6

    When I Plugged back into 2y'' + y' -y = 0 I get 2ae-x+1/2be1/2x -ae-x +1/2be1/2x -ae-x -be1/2x=0

    and theres nothing to cancel out :uhh:?

    Help?
     
  8. Sep 8, 2009 #7

    Mark44

    User Avatar
    Insights Author

    Staff: Mentor

    2ae-x+1/2be1/2x -ae-x +1/2be1/2x -ae-x -be1/2x = e-x(2a - a - a) + e.5x(.5b + .5b - b) = ?
     
  9. Sep 8, 2009 #8
    ahh totally 4got about that ex . . lets see what I can do now lol
     
  10. Sep 8, 2009 #9
    um I am still having some trouble with this . . cause even after factoring it your left with 2 unknown variables so how are you to prove it?
     
  11. Sep 8, 2009 #10
    Never Mind, I'm an idiot I already answered the Question lmao

    Thanks Guys.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?