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:
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?