Find the general solution of the given differential equation:
$$9y'' + 6y' + y = 0$$
Solve:
The characteristic polynomial is given by $9r^2 + 6r + 1 = 0$
Factor it we obtain $(3r + 1)(3r + 1)$
Then $r_1 = -\frac{1}{3}$ and $r_2 = -\frac{1}{3}$
We observe repeated roots here.
Then the general solution of the given differential equation is $y(t) = c_1e^{-\frac{1}{3} t} + c_2te^{-\frac{1}{3}t}$
