Questions from Calculus

Q: Sketch the solution of the differential equation. Also indicate the constant

Sketch the solution of the differential equation. Also indicate the constant solution. y’ = y3 - 6y2 + 9y, y(0) = - 1/4, y(0) = 1/4, y(0) = 4

Q: The birth rate in a certain city is 3.5%

The birth rate in a certain city is 3.5% per year, and the death rate is 2% per year. Also, there is a net movement of population out of the city at a steady rate of 3000 people per year. Let N = f (t...

Q: Suppose that in a chemical reaction, each gram of substance A

Suppose that in a chemical reaction, each gram of substance A combines with 3 grams of substance B to form 4 grams of substance C. The reaction begins with 10 grams of A, 15 grams of B, and 0 grams of...

Q: A bank account has $20,000 earning 5% interest

A bank account has $20,000 earning 5% interest compounded continuously. A pensioner uses the account to pay himself an annuity, drawing continuously at a $2000 annual rate. How long will it take for t...

Q: A continuous annuity of $12,000 per year is to

A continuous annuity of $12,000 per year is to be funded by steady withdrawals from a savings account that earns 6% interest compounded continuously. (a) What is the smallest initial amount in the acc...

Q: Let f (t) be the solution to y’ = 2e2t

Let f (t) be the solution to y’ = 2e2t-y, y(0) = 0. Use Euler’s method with n = 4 on 0 ≤ t ≤ 2 to estimate f (2). Then show that Euler’s method gives the exact value of f (2) by solving the different...

Q: The function f (t) = 5000/(1 + 49e

The function f (t) = 5000/(1 + 49e-t) is the solution of the differential equation y’ = .0002y(5000 - y) from Example 8. (a) Graph the function in the window [0, 10] by [-750, 5750]....

Q: Let f (t) be the solution to y’ = (

Let f (t) be the solution to y’ = (t + 1)/y, y(0) = 1. Use Euler’s method with n = 3 on 0 ≤ t ≤ 1 to estimate f (1). Then, show that Euler’s method gives the exact value of f (1) by solving the diffe...

Q: Use Euler’s method with n = 6 on the interval 0 ≤

Use Euler’s method with n = 6 on the interval 0 ≤ t ≤ 3 to approximate the solution f (t) to y’ = .1 y(20 - y), y(0) = 2.

Q: Use Euler’s method with n = 5 on the interval 0 ≤

Use Euler’s method with n = 5 on the interval 0 ≤ t ≤ 1 to approximate the solution f (t) to y’ = ½ y (y - 10), y(0) = 9.