Lesson 4.10d-e

4.10d-e Second order linear differential equations Quiz: OCR Further Maths, Unit 1

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

In partnership with Revision Ninja

Lesson 4.10d-e, Second order linear differential equations: 20 multiple choice questions for the OCR Further Maths (H245), Unit 1: Pure Core (Y540, Y541), written with Revision Ninja.

Host it live on the board and students join with a game code on their own devices, or revise alone with Free Play. The answers are revealed in the game.

Host this setFree Play

The 20 questions

  1. What is the auxiliary equation for the differential equation y'' - 5y' + 6y = 0?

    • m^2 + 5m + 6 = 0
    • m^2 + 6 = 0
    • m^2 - 5m + 6 = 0
    • m^2 - 5m = 0

  2. What complementary function form corresponds to distinct real roots r1 and r2?

    • (A + Bx) e^(r1 x)
    • A e^(r1 x) cos(r2 x)
    • e^(r1 x)(A cos x + B sin x)
    • A e^(r1 x) + B e^(r2 x)

  3. What complementary function form corresponds to a repeated real root r?

    • e^(rx)(A cos x + B sin x)
    • A e^(rx) + B e^(-rx)
    • (A + Bx) e^(rx)
    • A e^(rx) + B

  4. What term describes a linear differential equation whose right-hand side is equal to zero?

    • Particular
    • Non-homogeneous
    • Singular
    • Homogeneous

  5. Which type of damping occurs when the auxiliary equation has complex conjugate roots?

    • Zero damping
    • Critical damping
    • Overdamping
    • Underdamping

  6. How many initial conditions are required to find unique arbitrary constants for a second-order DE?

    • 3
    • 4
    • 2
    • 1

  7. What form of trial particular integral should be used for y'' + 4y = 3e^(2x)?

    • lambda x e^(2x)
    • lambda e^(2x)
    • lambda + mu e^(2x)
    • lambda e^(-2x)

  8. What are the roots of the auxiliary equation m^2 - 4m + 4 = 0?

    • Repeated root 2
    • Distinct roots 2 and -2
    • Complex roots 2 +/- 2i
    • Distinct roots 4 and 1

  9. What are the roots of the auxiliary equation m^2 + 9 = 0?

    • 3 repeated
    • +/- 3
    • +/- 3i
    • +/- 9i

  10. What is the complementary function for the differential equation y'' + 9y = 0?

    • A cos 9x + B sin 9x
    • (A + Bx) e^(3x)
    • A e^(3x) + B e^(-3x)
    • A cos 3x + B sin 3x

  11. What trial particular integral is suitable for y'' - y' - 2y = 4x + 1?

    • lambda x^2 + mu x
    • lambda x + mu
    • lambda x
    • lambda e^x

  12. What trial particular integral is suitable for the differential equation y'' + 2y' + 5y = 5 sin 2x?

    • a sin 2x + b cos 2x + c
    • a sin 2x + b cos 2x
    • ae^(2x)
    • a sin 2x

  13. What is the particular integral for the differential equation y'' + y = 5?

    • 5 e^x
    • 5
    • 0
    • 5x

  14. What condition on the discriminant b^2 - 4ac indicates an overdamped system?

    • b^2 - 4ac = 0
    • b^2 - 4ac < 0
    • b^2 - 4ac <= 0
    • b^2 - 4ac > 0

  15. What is the value of lambda in the particular integral y = lambda e^x for y'' + 4y = 10e^x?

    • 5
    • 2.5
    • 10
    • 2

  16. What trial particular integral should be used for y'' - 3y' + 2y = 4e^x?

    • lambda x e^x
    • lambda e^x
    • lambda e^(-x)
    • lambda x^2 e^x

  17. What is the angular frequency of oscillations described by y'' + 16y = 0?

    • 8 rad s^-1
    • 16 rad s^-1
    • 2 rad s^-1
    • 4 rad s^-1

  18. What is the general solution of the differential equation y'' - y = 0?

    • A e^x + B x
    • A e^x + B e^(-x)
    • A cos x + B sin x
    • (A + Bx) e^x

  19. What type of damping occurs in a second-order system when the discriminant b^2 - 4ac equals zero?

    • Critical damping
    • Overdamping
    • Underdamping
    • Light damping

  20. What is the particular integral for the differential equation y'' + 4y = 12?

    • y = 3x
    • y = 4
    • y = 3
    • y = 12

All OCR Further Maths quizzes