plumiSecond order differential equations: Edexcel International A Level Further Maths questions
Every Edexcel International A Level Further Maths exam question on FP2.5 Second order differential equations, 2019–2025, with its mark scheme and examiner’s report.
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All 13 questions on Second order differential equations, as a list
- June 2025, Further Pure 2 (FP2), Q4 (10 marks): Given that y = λxe 3x is a particular integral of the differential equation 4 11 3 78 2 2 3 d d d d e y x y x y x (a) determine the value of the constant λ (b)
- June 2025 (A), Further Pure 2 (FP2), Q7 (13 marks): (a) Show that the substitution x = e u, where u is a function of x, transforms the differential equation 2 3 27 2 2 2 2 x y x x y x y x d d d d x > 0 (I) into t
- January 2025, Further Pure 2 (FP2), Q6 (11 marks): (a) Determine the general solution of the differential equation 2 2 5 d 4 d d 4 37 6e d x y y y x x Given that y = 0 and d 0 d y x when x = 0 (b) determine the
- June 2024, Further Pure 2 (FP2), Q8 (10 marks): (a) Given that t = ln x, where x > 0, show that d d e d d d d 2 2 2 2 2 y x y t y t t (b) Hence show that the transformation t = ln x, where x > 0, trans
- January 2024, Further Pure 2 (FP2), Q6 (14 marks): The differential equation d d d d e 2 2 3 6 13 8 0 x t x t x t t describes the motion of a particle along the x‑axis. (a) Determine the general solution of th
- June 2023, Further Pure 2 (FP2), Q4 (11 marks): (a) Determine the general solution of the differential equation d d d d 2 2 2 8 16 48 34 y x y x y x Given that y = 4 and d d y x = 21 at x = 0 (b) determine th
- January 2023, Further Pure 2 (FP2), Q9 (13 marks): (a) Given that x = t 1 2 , determine, in terms of y and t, (i) d d y x (ii) d d 2 2 y x (b) Hence show that the transformation x = t 1 2 , where t > 0, transfor
- June 2022, Further Pure 2 (FP2), Q7 (12 marks): (a) Show that the transformation y = xv transforms the equation 3 d d 2 2 y x – 6 x d d y x + 6 2 y x + 3y = x2 x ≠ 0 (I) into the equation 3 d d 2 2 v x + 3v =
- January 2022, Further Pure 2 (FP2), Q2 (6 marks): Determine the general solution of the differential equation 2 5 3 2 2 2 3 d d d d e y x y x y x − − =
- October 2021, Further Pure 2 (FP2), Q7 (11 marks): (a) Show that the transformation x = t 2 transforms the differential equation 4x d d 2y x2 + 2 (1 + 2 x ) d d y x − 15y = 15x (I) into the differential equation
- June 2021, Further Pure 2 (FP2), Q6 (13 marks): (a) Find the general solution of the differential equation d d d d 2y x y x y x x 2 2 6 8 2 − + = + (b) Find the particular solution of this differential equati
- January 2021, Further Pure 2 (FP2), Q6 (12 marks): (a) Determine the general solution of the differential equation d d d d 2 2 2 5 6 y x y x y x + + = cos (b) Find the particular solution for which y = 0 and d d
- October 2020, Further Pure 2 (FP2), Q8 (14 marks): (a) Show that the transformation x = eu transforms the differential equation x2 d d 2 2 y x + 3x d d y x − 8y = 4 ln x x > 0 (I) into the differential equation
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