Here's the full text of the question:

**To see the effect of changing the parameter b in the initial value problem:** ** ** **Solve for , and and sketch the solutions.**
So basically, in short, we have the following IVPs:

1.

2.

3.

I already worked out all of them. For #1, I got

. For #2, I wound up with

. And lastly, for #3, I got

. I graphed all of these functions on my calculator to look for any similarities (I swear I didn't make any mistakes in doing so; I was extremely careful with the notation), but couldn't find any.

My question is this: what effect does changing the coefficient of the first derivative have on the solution of a second-order, linear, homogeneous ODE with constant coefficients, especially in my particular case?