Calculate value of variable from solution to a 2nd ODF

[blondii]

The Question:
Find the value of r such that v = x^r is a solution of

xd²v/dx² + (x+4)\frac{dv}{dx} + 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

 

[blondii]

The Question:
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.
Thanks

Just a little correction. After expanding the diff equation I get x^r(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

 

[who_]

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.

 

[blondii]

Thanks for the reply who. Much appreciated. Cheers