Exam 10: Introduction to Differential Equations

The differential equation can be solved by which of the following?

A deer population for a certain area is initially 350. After 2 years, the population increases to 650. Assuming logistic growth with a carrying capacity of 1200, how long after reaching 650 will it take the population to reach 1000?

A rat population for a certain field is initially . After 3 years, the population increases to 450. After another 2 years, the population increases to 650. Assuming logistic growth with a carrying capacity of 900, what is ?

Use Euler's method with step size to approximate where is the solution to the initial value problem .

Let be an increasing function passing through such that the length of the tangent line between the tangency point and the y-axis is . A) Find an initial value problem satisfied by . B) Use Euler's method with to approximate .

Consider the initial value problem . A) Use Euler's method with to approximate . Give your answer to six decimal places. B) Solve the initial value problem and find to six decimal places. C) Compute the error in approximating .

Solve the following differential equations. A) B) (Hint: rewrite for .)

The curves orthogonal to the solutions of are:

A deer population for a certain area is initially . After 6 years, the population increases to 250. After another 4 years, the population increases to 300. Assuming logistic growth with a carrying capacity of 400, what is ?

Solve the initial value problem.

The differential equation can be solved by which of the following?

Solve the differential equations using separation of variables. A) B)

Solve the initial value problems. A) B)

Solve the differential equation .

Twenty-five rabbits were brought to a zoo 15 years ago. At present there are 35 rabbits in the zoo. The zoo can support a maximum of 180 rabbits. Assuming a logistic growth model, when will the rabbit population reach 50, 100, and 180 rabbits?

Deer in a certain region, are born at a rate that is proportional to their current population. With the absence of outside factors, the population will double in 3 years' time. Each year 5 deer join the population, 10 are caught by hunters, and 4 die of natural causes. If initially there are 50 deer, will the population survive? If not, when will it die out?

A water tank is obtained by rotating the graph of for about the y-axis (assume length is measured in meters). The tank is filled with water and water drains through a circular hole of radius 1 cm at the bottom of the tank. How long does it take for the tank to empty?

Solve the differential equation .

Solve the initial value problems. A) B)

The differential equation can be solved by which of the following?