12. Numerical and Qualitative Methods

Qualitative Behavior Without Closed Forms — Quiz

Test your understanding of qualitative behavior without closed forms with 5 practice questions.

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Practice Questions

Question 1

What is an equilibrium solution of the autonomous differential equation $y'=f(y)$?

Question 2

For the differential equation $y'=y(2-y)$, which values are equilibrium solutions?

Question 3

For the differential equation $y'=y(2-y)$ and an initial value with $0<y<2$, what happens as $t$ increases?

Question 4

For the differential equation $y'=y(2-y)$, which equilibrium is stable?

Question 5

Suppose an autonomous differential equation satisfies $f(y)>0$ when $y<1$ and $f(y)<0$ when $y>1$. What qualitative behavior should solutions near $y=1$ show?