Math 212: Dierential Equations
Homework assignment 1
Dr. M. H. Mertens
Exercise 1.
Suppose that in some rural area, there is a population of eld mice whose growth is approximately proportional to the populations current size, i.e.,
dp
= rp,
dt
where p(t)
Math 212: Differential Equations
Homework assignment 4
Dr. M. H. Mertens
Exercise 1.
Show that any separable equation is also exact.
Solution. By definition, any separable equation can be written in the form
M (x) + N (y)y 0 = 0.
Since y
M (x) = 0 = x
N (