# Differential Equations

# Differential Equations: Slope Field of Dreams Quiz

Think you’ve got your head wrapped around

*? Put your knowledge to the test. Good luck — the Stickman is counting on you!***Differential Equations**Q. A solution

*y*to the differential equation

passes through the point (4,12). What is the slope of *y* at that point?

3

4

Q. Which of the following slope fields is generated by the differential equation

Q. Determine the differential equation that generated the following slope field:

Q. Below is the slope field corresponding to some differential equation. Which of the following could be a solution to the d.e. that goes through the point (-3,4)?

Q. How many solutions to the differential equation go through the point (2,2) ?

none

1

2

infinitely many

Q. Find all equilibrium solutions to the differential equation

*y*= ± 2

*y*= ± 4

*y*= ± 2,

*y*= 4

*y*= -2,

*y*= ± 4

Q. For which of the following differential equations is

*y*= 0 a stable equilibrium solution?Q. Find all unstable equilibrium solutions for the differential equation

This differential equation has no unstable equilibrium solutions.

*y*= 0

*y*= 3 and

*y*= -2

*y*= -3 and

*y*= 2

Q. A solution to the differential equation passes through the point

*P*. This solutionmust be concave up.

must be concave down.

may be horizontal depending on where

*P*is.is not a function because it fails the vertical line test.

Q. A solution to the differential equation

must be concave up.

must be concave down.

may be horizontal depending on where

*P*is.is not a function because it fails the vertical line test.