x' = sin(x), x(0) = 1
and x' = rx(1 - x/π), x(0) = 1
a. Find all of the fixed points of each of these two differential equations, and classify each one as stable or unstable. Use this to explain the similarities between the solutions you graphed on the previous homework.
b. Graph the two functions f(x) = sin(x) and g(x) = rx (1 – x/π). (You can choose a value of r, or try a few.) Where are the two graphs similar? Explain why the graphs being very similar only in that region is enough to make the solutions to the two differential equations above also very similar.
