Find the general solution of the given differential equation 9y''+9y'-4y=0
Solution: We can write as $9r^2+9r-4=0$. Then by factorization, we can get
(3r-1)(3r+4)=0, $r_1=\frac{1}{3}$ or $r_2=-\frac{4}{3}$, and these are two
distinct real roots, so the general solution is
$y=c_1e^{\frac{t}{3}}+c_2e^{-\frac{4t}{3}}$
