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Differential Equations Practice Test: printable

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Differential Equations Practice Test

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26 questions. Calculator allowed. Show your working. steplyclass.com/differential-equations/practice-test/

  1. 1

    Is y = e3x a solution of y' = 3y
    1. A) Yes
    2. B) No

  2. 2

    Is y = 3e2x − e3x a solution of y'' − 5y' + 6y = 0
    1. A) Yes
    2. B) No

  3. 3

    Solve dy/dx = 6x2

    Answer: ____________________

  4. 4

    Solve dy/dx = 2e3x + 1, y(0) = 2

    Answer: ____________________

  5. 5

    Solve dy/dx = 2xy

    Answer: ____________________

  6. 6

    Solve dy/dx = (x2 + 1)y

    Answer: ____________________

  7. 7

    Solve dy/dx = 2xy, y(0) = 3

    Answer: ____________________

  8. 8

    Solve dy/dx = 2y2, y(0) = −1

    Answer: ____________________

  9. 9

    dP/dt = 0.03P, P(0) = 500, find P(10)
    1. A) 674.93
    2. B) 500
    3. C) 6749.3
    4. D) 650

  10. 10

    dA/dt = 0.08A, A(0) = 2000, find A(12)

    Answer: ____________________

  11. 11

    dT/dt = −0.1(T − 20), T(0) = 90, find T(10)
    1. A) −457.5
    2. B) 45.75
    3. C) 90
    4. D) 33.11

  12. 12

    dT/dt = −0.25(T − 20), T(0) = 100, when is T = 30

    Answer: ____________________

  13. 13

    Solve y' + 2y = 4

    Answer: ____________________

  14. 14

    Solve y' − 2xy = 6x

    Answer: ____________________

  15. 15

    Use Euler's method on dy/dx = x + y, y(0) = 1, step 0.1, to find y(0.3)
    1. A) y(0.3) ≈ 1
    2. B) y(0.3) ≈ 1.2
    3. C) y(0.3) ≈ 3
    4. D) y(0.3) ≈ 1.362

  16. 16

    Use Euler's method on dy/dx = 3x − y, y(0) = 2, step 0.5, to find y(2)

    Answer: ____________________

  17. 17

    Solve y'' − 5y' + 6y = 0, y(0) = 2, y'(0) = 5

    Answer: ____________________

  18. 18

    Solve 2y'' + 3y' + y = 0, y(0) = 1, y'(0) = 0

    Answer: ____________________

  19. 19

    Solve y'' − 6y' + 9y = 0, y(0) = 2, y'(0) = 7

    Answer: ____________________

  20. 20

    Solve y'' + 6y' + 9y = 0, y(0) = 2, y'(0) = −5

    Answer: ____________________

  21. 21

    Laplace transform of 1

    Answer: ____________________

  22. 22

    Laplace transform of 3t2 − 4e5t + 2

    Answer: ____________________

  23. 23

    Find the inverse Laplace transform of 1/s.

    Answer: ____________________

  24. 24

    Find the inverse Laplace transform of 5/((s − 2)(s + 3)).

    Answer: ____________________

  25. 25

    Solve y' + 2y = 0, y(0) = 3 using Laplace

    Answer: ____________________

  26. 26

    Solve y' − 2y = 6e−t, y(0) = 0 using Laplace

    Answer: ____________________

Answer key

  1. A Yes
  2. A Yes
  3. y = 2x3 + C
  4. y = 23e3x + x + 43
  5. y = Aex²
  6. y = Ae1 over 3x³ + x
  7. y = 3ex²
  8. y = −1/(2x + 1)
  9. A 674.93
  10. 5223.39
  11. B 45.75
  12. t ≈ 8.32
  13. y = 2 + Ce−2x
  14. y = −3 + Cex²
  15. D y(0.3) ≈ 1.362
  16. y(2) ≈ 3.3125
  17. y = e2x + e3x
  18. y = −e−x + 2e−x2
  19. y = 2e3x + xe3x
  20. y = 2e−3x + xe−3x
  21. 1s
  22. 6s3 − 4/(s − 5) + 2s
  23. f(t) = 1
  24. f(t) = e2t − e−3t
  25. y = 3e−2t
  26. y = 2e2t − 2e−t

Every answer solved step by step: steplyclass.com/differential-equations/practice-test/answers/