AP Calculus AB Exam Test- Differential Equations

1. Which of the following is a solution to the differential equation dy/dx = 2x?

(a) y = x^2 + 1

(b) y = 2x + 1

(c) y = 2x^2 + 1

d) y = 2x^3 + 1

2. What is the solution to the initial value problem dy/dx = 3x^2, y(0) = 2?

(a) y = x^3 + 2

(b) y = 3x^3 + 2

(c) y = 3x^2 + 2

(d) y = 2x^2 + 3

3. Which of the following is a particular solution to the differential equation dy/dx = e^x?

(a) y = e^x – 1

(b) y = e^x + 1

(c) y = e^x + C

(d) y = e^(x^2)

4. Which of the following is the solution to the differential equation dy/dx = -2y?

(a) y = e^(-2x)

(b) y = e^(2x)

c) y = -2e^x

(d) y = -2e^(-x)

5. Which of the following is a solution to the differential equation dy/dx = 1/x?

(a) y = ln(x) + C

(b) y = x ln(x) + C

(c) y = 1/x + C

(d) y = x + C

6. Which of the following is a solution to the initial value problem dy/dx = 2x, y(1) = 3?

(a) y = x^2 + 3

(b) y = 2x + 3

(c) y = 2x^2 + 3

(d) y = 2x^2 + 1

7. Which of the following is a particular solution to the differential equation dy/dx = 2x^3?

(a) y = x^4

(b) y = x^4 + C

(c) y = x^3 + C

(d) y = 2x^4

AP Calculus AB - Differential Equations- 7 Questions