plumiDifferential equations: WJEC A‑Level Further Maths questions
Every WJEC A-Level Further Maths exam question on 4.8 Differential equations, 2018–2025, with its mark scheme and examiner’s report.
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All 9 questions on Differential equations, as a list
- Summer 2025, Unit 4, Q6 (8 marks): 6. Solve the differential equation d y cos x d y sin x , x y 3 x 0 when given that . [8]
- Summer 2025, Unit 4, Q9 (11 marks): 9. Find the solution of the differential equation 2 d y 16 y 3sin x , 2 d x where (π, 3) is a stationary point. [11]
- Summer 2024, Unit 4, Q3 (9 marks): 3. Given the differential equation d y cos x y sin x 4cos 3 x sin x 5 x d x , find an equation for y in terms of x. y 3 2 and when [9] 4
- Summer 2024, Unit 4, Q10 (12 marks): 10. The following simultaneous equations are to be solved. d x 3 t t 4 x 2 y 6e d d y 3 6 x 8 y 15e t t d d 2 x d x 12 20 x 0 (a) Show that .
- Summer 2023, Unit 4, Q9 (8 marks): 9. Consider the differential equation ) dy )2 , ( ( x +1 dx + 5y = x +1 x > −1. y = 1 Given that when x = 1, find the value of y when x = 0. [8] 4
- Summer 2023, Unit 4, Q13 (17 marks): 13. Two species of insects, X and Y, co-exist on an island. The populations of the species at time t years are x and y respectively, where x and y are measured
- Summer 2022, Unit 4, Q12 (12 marks): 12. Find the solution of the differential equation 3 d2y dx2 + 5 dy dx − 2y = 8 + 6x − 2x2 , dy dx = 5 where y = 6 and when x = 0. [12]
- Summer 2019, Unit 4, Q6 (10 marks): 6. Solve the differential equation d2y dx2 − 7 dy dx + 10y = 0, d2y dy dx = 1 dx2 = 8 x = 0 where and when . [10]
- Summer 2019, Unit 4, Q10 (8 marks): 10. Given the differential equation dy sec x + y cosecx = 2 dx x = π x = π and when y = 3, find the value of y when . [8] 4 2
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