plumiDifferential equations: OCR MEI A‑Level Further Maths questions
Every OCR MEI A-Level Further Maths exam question on CP.9 Differential equations, 2018–2025, with its mark scheme and examiner’s report.
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![June 2024 Core Pure, question 14: d y d y - . e x 14 (a) Find the general solution of the differential equation 2 y 12 [7] 2 + - = d x d x d = y You are given that y tends to zero as x tends to](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/y42001-jun24-14-qp.webp?v=3)
![June 2023 Core Pure, question 11: y d - 11 Solve the differential equation cosh x x 2 y sinh x cosh x , given that y = when x 1 0 . [7] = = d](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/y42001-jun23-11-qp.webp?v=3)
![June 2022 Core Pure, question 12: d y 2 12 Solve the differential equation ( x xy given that y = 1 when x = 0, giving your 4 ) 1 , - - = d x answer in the form y = f (x). [9]](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/y42001-jun22-12-qp.webp?v=3)
![November 2021 Core Pure, question 13: d y d y ex 13 Find the general solution of the differential equation x 2 3 y 2 . [7] + - = d x 2 d](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/y42001-nov21-13-qp.webp?v=3)
![November 2020 Core Pure, question 14: Solve the simultaneous differential equations d + y d + x 2 x 4 y , 3 x 5 y , = = d t d t given that when t = 0, x = 0 and y = 1. [11]](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/y42001-nov20-14-qp.webp?v=3)
All 13 questions on Differential equations, as a list
- June 2025, Core Pure, Q13 (11 marks): y d 2 13 The gradient of a curve y f ( ) x satisfies the differential equation x x 2 y 2 x . = - = + d - . (a) Show that the integrating factor for this differe
- June 2025, Core Pure, Q17 (18 marks): A researcher is modelling the height of a particular type of tree over its lifetime. Data suggests that the maximum possible height of this type of tree over it
- June 2024, Core Pure, Q14 (12 marks): d y d y - . e x 14 (a) Find the general solution of the differential equation 2 y 12 [7] 2 + - = d x d x d = y You are given that y tends to zero as x tends to
- June 2024, Core Pure, Q17 (20 marks): In an industrial process, a container initially contains 1000 litres of liquid. Liquid is drawn from the bottom of the container at a rate of 5 litres per minut
- June 2023, Core Pure, Q11 (7 marks): y d - 11 Solve the differential equation cosh x x 2 y sinh x cosh x , given that y = when x 1 0 . [7] = = d
- June 2023, Core Pure, Q17 (24 marks): Two similar species, X and Y, of a small mammal compete for food and habitat. A model of this competition assumes, in a particular area, the following. • In the
- June 2022, Core Pure, Q12 (9 marks): d y 2 12 Solve the differential equation ( x xy given that y = 1 when x = 0, giving your 4 ) 1 , - - = d x answer in the form y = f (x). [9]
- June 2022, Core Pure, Q15 (23 marks): In an oscillating system, a particle of mass m kg moves in a horizontal line. Its displacement from - , and it is acted on by its equilibrium position O at time
- November 2021, Core Pure, Q13 (7 marks): d y d y ex 13 Find the general solution of the differential equation x 2 3 y 2 . [7] + - = d x 2 d
- November 2021, Core Pure, Q17 (20 marks): In a chemical process, a vessel contains 1 litre of pure water. A liquid chemical is then passed into the top of the vessel at a constant rate of a litres per m
- November 2020, Core Pure, Q14 (11 marks): Solve the simultaneous differential equations d + y d + x 2 x 4 y , 3 x 5 y , = = d t d t given that when t = 0, x = 0 and y = 1. [11]
- November 2020, Core Pure, Q16 (25 marks): The population density P, in suitable units, of a certain bacterium at time t hours is to be modelled by a differential equation. Initially, the population dens
- June 2019, Core Pure, Q17 (22 marks): A cyclist accelerates from rest for 5 seconds then brakes for 5 seconds, coming to rest at the end of the 10 seconds. The total mass of the cycle and rider is m
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