Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and beginning April 20th, 2021 (Eastern Time) the Yahoo Answers website will be in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.
Trending News
Find the general solution of this 2nd order linear ODE: (t^2)y"(t) - 5ty'(t) + 9y(t) = 0?
(t^2)y"(t) - 5ty'(t) + 9y(t) = 0
Is it even linear if the terms are multiplied like that? I want to know if I'm allowed to solve this with the method of undetermined coefficients?
1 Answer
- kbLv 77 years agoFavorite Answer
This is linear since we are multiplying by t (not y).
In fact, this is a Cauchy-Euler DE.
Assume that y = t^n for some constant n.
So, y' = nt^(n-1) and y'' = n(n-1) t^(n-2).
Substituting this into the DE yields
t^2 * n(n-1)t^(n-2) - 5t * nt^(n-1) + 9 * t^n = 0
==> (n(n-1) - 5n + 9) t^n = 0
==> n^2 - 6n + 9 = 0
==> (n - 3)^2 = 0
==> n = 3, 3.
So, a general solution is y = t^3 (A + B ln t).
Link:
http://en.wikipedia.org/wiki/Cauchy%E2%80%93Euler_...
I hope this helps!
