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Differential equations: CAIE A‑Level Further Maths questions

Every CAIE A-Level Further Maths exam question on 2.6 Differential equations, June 2024 and the specimen papers, with its mark scheme and examiner’s report.

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56 questions

  1. Q6

    June 2024 · Paper 2

    12 marks2.6 Differential equations2.1 Hyperbolic functions
    The whole paper ↗
    June 2024 Paper 2, question 6: ` j 1 6 (a) Show that cosh x sinh x e x 1 . [2] + 2 = 2 (b) Find the particular solution of the differential equation d 2 y d y ` j , 1 3 y 5 cosh x sinh x + +

  2. Q7

    June 2024 · Paper 2

    12 marks2.6 Differential equations2.4 Integration
    The whole paper ↗
    June 2024 Paper 2, question 7: (a) Use the substitution u 1 x 2 to find = + y x d x . [2] 1 x 2 + (b) Find the solution of the differential equation d y x x y x 2 sinh - 1 x , - = d = ` j. gi

  3. Q1

    Specimen · Paper 2

    6 marks2.6 Differential equations
    No published mark scheme
    The whole paper ↗
    Specimen Paper 2, question 1: Find the general solution of the differential equation d 2 x d x + d 4 + 4x = 7 – 2t2. [6] d t 2 t

  4. Q3

    Specimen · Paper 2

    8 marks2.6 Differential equations
    No published mark scheme
    The whole paper ↗
    Specimen Paper 2, question 3: Find the solution of the differential equation d y + 3y = sin x xd x x 1 π. Give your answer in the form y = f(x). for which y = 0 when x = 2 [8]
All 4 questions on Differential equations, as a list
  1. June 2024, Paper 2, Q6 (12 marks): ` j 1 6 (a) Show that cosh x sinh x e x 1 . [2] + 2 = 2 (b) Find the particular solution of the differential equation d 2 y d y ` j , 1 3 y 5 cosh x sinh x + +
  2. June 2024, Paper 2, Q7 (12 marks): (a) Use the substitution u 1 x 2 to find = + y x d x . [2] 1 x 2 + (b) Find the solution of the differential equation d y x x y x 2 sinh - 1 x , - = d = ` j. gi
  3. Specimen, Paper 2, Q1 (6 marks): Find the general solution of the differential equation d 2 x d x + d 4 + 4x = 7 – 2t2. [6] d t 2 t
  4. Specimen, Paper 2, Q3 (8 marks): Find the solution of the differential equation d y + 3y = sin x xd x x 1 π. Give your answer in the form y = f(x). for which y = 0 when x = 2 [8]

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