# Homework Help: Finding general soln of differential eqn (zero under the root)

1. Apr 26, 2010

### darryw

1. The problem statement, all variables and given/known data

9y'' + 6y' + y = 0

r^2 + 6r + 1

( -6 +/- root 36 - 36 ) / 18

lamda = -6/18 = -(2/9)
mu = 0

(this is the part im unsure about, because if i end up with a zero under the root, then does this make the final equation into this:

y = c_1*cos(0*x) + c_2*sin(0*x)

thanks for any help.
2. Relevant equations

3. The attempt at a solution

2. Apr 26, 2010

### gabbagabbahey

First, $-\frac{6}{18}=-\frac{1}{3}\neq-\frac{2}{9}[/tex]. Second, when you have a double root, [itex]\lambda$, you look for a solution of the form $y(t)=C_1e^{\lambda t}+C_2 t e^{\lambda t}$