Finding general soln of differential eqn (zero under the root)

[darryw]

Homework Statement

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

r^2 + 6r + 1

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

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

(this is the part I am 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.

Homework Equations

The Attempt at a Solution

 

[gabbagabbahey]

First, [itex]-\frac{6}{18}=-\frac{1}{3}\neq-\frac{2}{9}[/tex].

Second, when you have a double root, $\lambda$, you look for a solution of the form $y(t)=C_1e^{\lambda t}+C_2 t e^{\lambda t}$