Differential Equations Practice Test
26 questions from 13 lessons · 80 minutes · percent score and grade · step-by-step answers
How it works
- 26 questions, about 80 minutes (a timer counts down; you can hide it). Solve it right here: no sign-up.
- 5 questions have choices. For the others you type the answer: a number like 4, −2, 7/2 or 3.5, or for example x = 4, x = 2 or x = −3, (3, 5), 2x + 1. Use ^ for powers (x^2) and sqrt for √. Any form with the same value counts (7/2 = 3.5).
- One question at a time: Back, Next, Mark for review and the question list at the bottom. A calculator is on the screen.
- At the end: your percent and grade, every question right or wrong, why a wrong choice is wrong, and its step-by-step solution. Then practise these lessons next: the lessons of the questions you got wrong, with new questions.
Your answers and results are kept in this browser only, so you can close the page and come back.
Formulas: the Differential Equations formula sheet.
1 Question 1
Is y = e3x a solution of y' = 3y- A) Yes
- B) No
2 Question 2
Is y = 3e2x − e3x a solution of y'' − 5y' + 6y = 0- A) Yes
- B) No
3 Question 3
Solve dy/dx = 6x2Type the answer.
4 Question 4
Solve dy/dx = 2e3x + 1, y(0) = 2Type the answer.
5 Question 5
Solve dy/dx = 2xyType the answer.
6 Question 6
Solve dy/dx = (x2 + 1)yType the answer.
7 Question 7
Solve dy/dx = 2xy, y(0) = 3Type the answer.
8 Question 8
Solve dy/dx = 2y2, y(0) = −1Type the answer.
9 Question 9
dP/dt = 0.03P, P(0) = 500, find P(10)- A) 674.93
- B) 500
- C) 6749.3
- D) 650
10 Question 10
dA/dt = 0.08A, A(0) = 2000, find A(12)Type the answer.
11 Question 11
dT/dt = −0.1(T − 20), T(0) = 90, find T(10)- A) −457.5
- B) 45.75
- C) 90
- D) 33.11
12 Question 12
dT/dt = −0.25(T − 20), T(0) = 100, when is T = 30Type the answer.
13 Question 13
Solve y' + 2y = 4Type the answer.
14 Question 14
Solve y' − 2xy = 6xType the answer.
15 Question 15
Use Euler's method on dy/dx = x + y, y(0) = 1, step 0.1, to find y(0.3)- A) y(0.3) ≈ 1
- B) y(0.3) ≈ 1.2
- C) y(0.3) ≈ 3
- D) y(0.3) ≈ 1.362
16 Question 16
Use Euler's method on dy/dx = 3x − y, y(0) = 2, step 0.5, to find y(2)Type the answer.
17 Question 17
Solve y'' − 5y' + 6y = 0, y(0) = 2, y'(0) = 5Type the answer.
18 Question 18
Solve 2y'' + 3y' + y = 0, y(0) = 1, y'(0) = 0Type the answer.
19 Question 19
Solve y'' − 6y' + 9y = 0, y(0) = 2, y'(0) = 7Type the answer.
20 Question 20
Solve y'' + 6y' + 9y = 0, y(0) = 2, y'(0) = −5Type the answer.
21 Question 21
Laplace transform of 1Type the answer.
22 Question 22
Laplace transform of 3t2 − 4e5t + 2Type the answer.
23 Question 23
Find the inverse Laplace transform of 1/s.Type the answer.
24 Question 24
Find the inverse Laplace transform of 5/((s − 2)(s + 3)).Type the answer.
25 Question 25
Solve y' + 2y = 0, y(0) = 3 using LaplaceType the answer.
26 Question 26
Solve y' − 2y = 6e−t, y(0) = 0 using LaplaceType the answer.