Homework for §2.2
Find all critical points (equilibrium solutions) of the autonomous first order equations below,
and classify each as either stable or unstable.
dx
= −x2 + 7x − 10
dt
dx
= x3 − 5x2 + 3x + 9
2.
dt
[Hint: To find equilibrium solutions, you might do so graphically, or you might use the rational
root theorem along with long or synthetic division. We’ll use the latter method often in later
sections.]
1.
dx
= cos x
dt
.........................................................................................
3.
4. Construct a bifurcation diagram for the equation
dx
= x2 − 3kx + 2k 2 .
dt
Remember to use dotted lines to indicate unstable equilibria and solid lines for stable.