I just wanted to send a few comments about WeBWorK assignment 5b. The problem consists of three parts – in the first part, we use Euler’s method to generate a sequence of approximate values of y for various values of t (in my version of the problem it’s t=0, t=0.2, t=0.4, t=0.6, t=0.8, and t=1). Of course, these values are not exactly correct – they are approximations.
In parts b and c of the problem, we compare the approximate values with the actual values – this will give you some idea of how effective Euler’s method is. In part b, we find the actual solution to the differential equation (using the techniques from Exam #1). In part c, we compare (for various values of t), the actual value, given by the solution we found in part b, and the approximate value found in part a. To compare, we subtract the approximate value from the actual value (and then take the absolute value, since we don’t care about positive or negative, we only care about how far apart they are).
One more comment about notation: the symbol y with a dot over it means the same thing as y’, or dy/dt – that is, it means the derivative of y. This is fairly common notation, but we have not previously run into it this semester.
I hope this helps clear up confusion about parts b and c – let me know if you have questions.