This problem has multiple parts. After you submit your answers, you will be given the option to move on to the next part. I suggest that you print each page so that you can refer to them if necessary.

Throughout this WeBWork problem, let $a,b,$ and $c$ be real numbers with $a \neq 0$. In this exercise we will discover a method that will allow us to solve linear homogeneous differential equations of the form $$a\frac{d^2y}{dx^2}+b\frac{dy}{dx}+cy=0.$$

To solve this equation, we will assume that the solution $y$ of the differential equation is of the form $y=e^{mx}$ where $m$ is some number that we need to find. If we substitute $y=e^{mx}$ into $a\frac{d^2y}{dx^2}+b\frac{dy}{dx}+cy=0$, we find that

$0=a\frac{d^2y}{dx^2}+b\frac{dy}{dx}+cy$

$\hskip 48pt =e^{mx}\Big($

$\Big)$