Questions from Calculus

Q: Suppose that f (t) is a solution of y’ =

Suppose that f (t) is a solution of y’ = t2 - y2 and the graph of f (t) passes through the point (2, 3). Find the slope of the graph when t = 2.

Q: Find two constant solutions of y’ = 4y (y - 7

Find two constant solutions of y’ = 4y (y - 7).

Q: Figure 8 shows a portion of the solution curve of the differential

Figure 8 shows a portion of the solution curve of the differential equation y’ = 2y (1 - y) through the point (0, 2). On Fig. 8 or a copy of it, draw an approximation of the solution...

Q: Suppose that f (t) satisfies the initial-value problem

Suppose that f (t) satisfies the initial-value problem y = y2 + ty - 7, y(0) = 3. Is f (t) increasing or decreasing at t = 0?

Q: What is the slope field?

What is the slope field?

Q: Describe the separation-of-variables technique for obtaining the solution

Describe the separation-of-variables technique for obtaining the solution to a differential equation.

Q: What is a first-order linear differential equation?

What is a first-order linear differential equation?

Q: What is an integrating factor and how does it help you solve

What is an integrating factor and how does it help you solve a first-order linear differential equation?

Q: What is an autonomous differential equation?

What is an autonomous differential equation?

Q: How do you recognize an autonomous differential equation from its slope field

How do you recognize an autonomous differential equation from its slope field?