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Differential Equations

Differential Equations

Differential Equations: Slope Field of Dreams True or False

1. A solution y to the differential equation

passes through the point (4,12). What is the slope of y at that point? -> 3

2. Which of the following slope fields is generated by the differential equation ->
3. Determine the differential equation that generated the following slope field:


4. 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)?


5. How many solutions to the differential equation go through the point (2,2) ? -> none
6. Find all equilibrium solutions to the differential equation -> y = ± 2, y = 4
7. For which of the following differential equations is y = 0 a stable equilibrium solution? ->
8. Find all unstable equilibrium solutions for the differential equation -> This differential equation has no unstable equilibrium solutions.
9. A solution to the differential equation passes through the point P. This solution -> must be concave up.
10. A solution to the differential equation  

-> is not a function because it fails the vertical line test.