Deck 6: Section 5: Differential Equations

Question 1

Find the particular solution of the differential equation passing through the point .

A)
B)
C)
D)
E)

Answer 1

Question 2

Suppose an eight-pound object is dropped from a height of 5000 feet, where the air resistance is proportional to the velocity. Write the velocity as a function of time if its velocity after 7 seconds is approximately -75 feet per second. Use a graphing utility or a computer algebra system. Round numerical answers in your answer to four places.

A)
B)
C) 0.8018
D)
E)

Answer 2

Question 3

A 200-gallon tank is half full of distilled water. At time , a solution containing 0.5 pound of concentrate per gallon enters the tank at the rate of 5 gallons per minute, and the well-stirred mixture is withdrawn at the rate of 3 gallons per minute. At the time the tank is full, how many pounds of concentrate will it contain? Round your answer to two decimal places.

A) 11.61 lbs
B) 64.64 lbs
C) 71.34 lbs
D) 49.39 lbs
E) 82.32 lbs

Answer 3

82.32 lbs

Question 4

A 300-gallon tank is half full of distilled water. At time , a solution containing 0.5 pound of concentrate per gallon enters the tank at the rate of 8 gallons per minute, and the well-stirred mixture is withdrawn at the rate of 6 gallons per minute. At what time will the tank be full?

A) 150 minutes
B) 76 minutes
C) 75 minutes
D) 301 minutes
E) 600 minutes

Question 5

Find the particular solution of the differential equation that satisfies the boundary condition .

A)
B)
C)
D)
E)

Question 6

Solve the Bernoulli differential equation .

A)
B)
C)
D)
E)

Question 7

A 200-gallon tank is full of a solution containing 25 pounds of concentrate. Starting at time , distilled water is added to the tank at a rate of 10 gallons per minute, and the well-stirred solution is withdrawn at the same rate. Find the time at which the amount of concentrate in the tank reaches 15 pounds. Round your answer to one decimal place.

A) 18.3 min
B) 3.6 min
C) 20.4 min
D) 10.2 min
E) 5.1 min

Question 8

Solve the first order linear differential equation.

A)
B)
C)
D)
E)

Question 9

Solve the first-order linear differential equation .

A)
B)
C)
D)
E)

Question 10

Use as a integrating factor to find the general solution of the differential equation .

A)
B)
C)
D)
E)

Question 11

Find the particular solution of the differential equation that satisfies the initial condition .

A)
B)
C)
D)
E)

Question 12

Assume an object weighing 7 pounds is dropped from a height of 9,000 feet, where the air resistance is proportional to the velocity. Round numerical answers in your answer to two places. (i) Write the velocity as a function of time if the object's velocity after 6 seconds is 3.50 feet per second.
(ii) What is the limiting value of the velocity function?

A) (i) ; (ii) 0
B) (i) ; (ii) 0
C) (i) ; (ii) 3.5000
D) (i) ; (ii) 3.5000
E) (i) ; (ii) limit does not exist

Question 13

Find the particular solution of the differential equation that satisfies the boundary condition .

A)
B)
C)
D)
E)

Question 14

Find the particular solution of the differential equation that satisfies the boundary condition .

A)
B)
C)
D)
E)

Question 15

Solve the first order linear differential equation.

A)
B)
C)
D)
E)

Question 16

A 100-gallon tank is full of a solution containing 25 pounds of concentrate. Starting at time , distilled water is added to the tank at a rate of 10 gallons per minute, and the well-stirred solution is withdrawn at the same rate. Find the quantity of the concentrate in the solution as .

A) 10
B) 26
C) 25
D) 0
E) 1

Question 17

A 300-gallon tank is full of a solution containing 35 pounds of concentrate. Starting at time distilled water is added to the tank at a rate of 30 gallons per minute, and the well-stirred solution is withdrawn at the same rate. Find the amount of concentrate Q in the solution as a function of t.

A)
B)
C)
D)
E)