# Thread: How to solve the following ODE using method of undetermined coefficients

1. ## How to solve the following ODE using method of undetermined coefficients

q'' + 4q' +3q

2. ## Re: How to solve the following ODE using method of undetermined coefficients

the method of undetermined coefficients is used when you have a driving function.

If you just want the homogeneous solution the method doesn't enter into it.

Just find the roots $r_1, r_2$ of the characteristic equation

$s^2 + 4s + 3=0$

and the solutions will be

$q(x) = c_1 e^{r_1 x} + c_2 e^{r_2 x},~c_1, c_2 \in \mathbb{C}$

In this case

$(s+3)(s+1)=0$

$r_1 = -3,~r_2 = -1$

$q(x) = c_1 e^{-3x}+c_2 e^{-x}, c_2 \in \mathbb{C}$