But first, the original problem. So you know what I'm talking about. (Yeah, sure.)
"One or more initial conditions are given for each differential equation in the following exercises. Use the qualitative theory of autonomous differential equations (huh?) to sketch the graphs of the corresponding solutions. Include a yz-graph if one is not already provided. Always indicate the constant solutions on the ty-graph whether they are mentioned or not."
y' = 3 - 1/2y, y(0) - 4, y(0) = 8.
The solution:
