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Calculate value of variable from solution to a 2nd ODF

  1. Jul 27, 2012 #1
    The Question:
    Find the value of r such that v = xr is a solution of

    xd2v/dx2 + (x+4)[itex]\frac{dv}{dx}[/itex] + 3v = 0

    My Solution:

    After finding the 1st and 2nd derivative of v and substituting into the equation to equat to zero and look for r, I get the answer r =-3. I also get a root that is undefined. I just want someone to confirm my answer or let me know if there is a better method to solve for r. Could their be a possibility of an error in the question?

    Thanks
     
  2. jcsd
  3. Jul 27, 2012 #2
    Just a little correction. After expanding the diff equation I get xr(rx-1+1)(3+r) = 0

    The answers are r = -3, r = -x or r = undefined.

    Please advise if I am on the right track.

    Thanks
     
  4. Jul 28, 2012 #3
    You are on the right track. Be sure, however, to treat the cases where r = 1 and r = 2 separately; think about why you should :)

    On the other hand, what doe r = -x or undefined mean? r should be a value independent of x. And saying that r = undefined is undefined and has no meaning. So r = -3 is indeed the solution.
     
  5. Jul 28, 2012 #4
    Thanks for the reply who. Much appreciated. Cheers
     
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