Lesson 1.08k

1.08k Differential equations by integration Quiz: OCR Maths, Unit 8

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson 1.08k, Differential equations by integration: 20 multiple choice questions for the OCR Maths (H240), Unit 8: Integration, written with Revision Ninja.

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The 20 questions

  1. What is the first step when solving the differential equation dy/dx = f(x)g(y)?

    • Differentiate both sides
    • Apply product rule
    • Separate variables
    • Square both sides

  2. What is the general solution of dy/dx = 2x?

    • y = 2 + C
    • y = x^2
    • y = x^2 + C
    • y = x^2/2 + C

  3. What is the general solution of dy/dx = y?

    • y = ln x + C
    • y = A e^x
    • y = e^(x^2)
    • y = x e^x + C

  4. What does substituting an initial condition into a general solution determine?

    • Particular solution
    • Integrating factor
    • General solution
    • Gradient vector

  5. Separating the variables in dy/dx = x/y gives which equation?

    • dy/y = dx/x
    • x dy = y dx
    • y dy = x dx
    • y dy = dx

  6. How many arbitrary constants are in the general solution of a first-order differential equation?

    • Two
    • One
    • Infinitely many
    • Zero

  7. Solve dy/dx = 3x^2 y with y(0) = 1.

    • y = x^3 + 1
    • y = e^(x^3)
    • y = e^(3x^2)
    • y = 3 e^(x^3)

  8. Solve dy/dx = x/y with y(0) = 2.

    • y = x + 2
    • y = x^2 + 4
    • y = sqrt(x^2 - 4)
    • y = sqrt(x^2 + 4)

  9. Solve dy/dx = cos x / (2y) with y(0) = 1.

    • y = 1 + sin x
    • y = sqrt(1 - sin x)
    • y = sqrt(1 + sin x)
    • y = (1 + sin x)/2

  10. A population satisfies dP/dt = 0.05 P with P(0) = 200. Approximately what is P when t = 10?

    • 300.0
    • 329.7
    • 210.3
    • 421.3

  11. Solve dT/dt = -0.1 (T - 20) with T(0) = 100.

    • T = 20 - 80 e^(-0.1t)
    • T = 20 + 80 e^(-0.1t)
    • T = 20 + 100 e^(-0.1t)
    • T = 100 e^(-0.1t)

  12. What is the particular solution of dy/dx = 4y with y(0) = 5?

    • y = 5 e^(4x)
    • y = 4 e^(5x)
    • y = 5 + 4x
    • y = e^(4x) + 5

  13. What is the general solution of dy/dx = -y/x for x > 0?

    • y = ln x + A
    • y = -A/x^2
    • y = A/x
    • y = A x

  14. Solve dy/dx = x y^2 with y(0) = 1, and give the particular solution.

    • y = 1/(1 - x^2)
    • y = 2/(2 + x^2)
    • y = 2/(2 - x^2)
    • y = 1 + x^2/2

  15. Solve dy/dx = 2x/y with y(1) = 3.

    • y = 2x^2 + 7
    • y = sqrt(x^2 + 7)
    • y = sqrt(2x^2 + 7)
    • y = sqrt(2x^2 - 7)

  16. A velocity satisfies dv/dt = -0.2 v with v(0) = 30 m/s. Approximately what is v when t = 5?

    • 15.0 m/s
    • 11.0 m/s
    • 24.0 m/s
    • 6.0 m/s

  17. Find the general solution of dy/dx = e^(x+y).

    • e^x + e^y = C
    • e^(x+y) = C
    • e^x + e^(-y) = C
    • e^x - e^(-y) = C

  18. Solve dy/dx = (1 + y^2) x with y(0) = 0.

    • y = sin(x^2/2)
    • y = x^2/2
    • y = tan(x^2/2)
    • y = tan(x)/2

  19. The model dv/dt = 10 - 0.5 v with v(0) = 0 has solution v = 20 - 20 e^(-0.5t). What is the limiting speed as t tends to infinity?

    • 40
    • 0.5
    • 10
    • 20

  20. Solve dy/dx = x (y - 1) with y(0) = 3.

    • y = 1 + 2 e^(x^2)
    • y = 3 e^(x^2/2)
    • y = 1 + x^2
    • y = 1 + 2 e^(x^2/2)

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