FINALS EXAM IN DE

1. Obtain the differential equation of the family of all parabolas whose vertices are at the origin and whose axes are horizontal.

➢ y/2x

2. On a day when the temperature is 30° Celsius, a cool drink is taken from a refrigerator whose temperature is 5°. If the temperature of the drink is 20° after 10 minutes, what will its temperature be after 35 minutes?

➢ 29

3. Environmentalist predict that in t years the deer population in a forest will obey the

logistic equation P(t )= 20

1+ 4 e^−2t

, where P is the number of deer in thousands. What is

the differential equation that describes the deer population growth rate?

➢ 160e^(2t)/(e^2t + 4)^2