plumiFirst order differential equations: Edexcel International A Level Further Maths questions
Every Edexcel International A Level Further Maths exam question on FP2.4 First order differential equations, 2019–2025, with its mark scheme and examiner’s report.
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All 13 questions on First order differential equations, as a list
- June 2025, Further Pure 2 (FP2), Q6 (11 marks): (a) Show that the substitution z = 1 2y transforms the differential equation 2 0 3 d d y x x y x x y (cot ) (tan sec ) 0 < x < 2 π (I) into the differential equ
- June 2025 (A), Further Pure 2 (FP2), Q2 (8 marks): (a) Show that the differential equation (x + 2) d d y x = 3x 2 + 6x – y x ≠ –2 can be written in the form d d y x + f (x) y = kx where f is a function to be det
- January 2025, Further Pure 2 (FP2), Q1 (6 marks): 2 d 3 tan sec d y y x x x (a) Show that an integrating factor for this differential equation is given by p(x) = cos 3 x Given that y = 4 when x = π 4 (b) determ
- June 2024, Further Pure 2 (FP2), Q4 (9 marks): (a) Show that the substitution y t 2 1 = transforms the differential equation d d y x y xy 3 (I) into the differential equation d d t x t x 2 2 (II) (b) Solve d
- January 2024, Further Pure 2 (FP2), Q8 (13 marks): (a) For all the values of x where the identity is defined, prove that cot 2x + tan x ≡ cosec 2x (b) Show that the substitution y 2 = w sin 2x, where w is a func
- June 2023, Further Pure 2 (FP2), Q7 (11 marks): (a) Show that the substitution z = y –2 transforms the differential equation x y x y x y x d d 4 0 2 3 ln x > 0 (I) into the differential equation d d z x z x x
- January 2023, Further Pure 2 (FP2), Q3 (9 marks): (a) Show that the transformation y = 1 z transforms the differential equation x y x xy y 2 2 2 d d + = (I) into the differential equation d d z x z x x − = −2 2
- June 2022, Further Pure 2 (FP2), Q4 (7 marks): (a) Determine the general solution of the differential equation d d y x – 3 y tan x = e4x sec3 x giving your answer in the form y = f(x) (b) Determine the parti
- January 2022, Further Pure 2 (FP2), Q8 (14 marks): (a) Show that the transformation v = y – 2x transforms the differential equation d d y x + 2yx(y – 4x) = 2 – 8x 3 (I) into the differential equation d d v x = –
- October 2021, Further Pure 2 (FP2), Q4 (9 marks): (a) Determine the general solution of the differential equation (x + 1) d d y x − xy = e3x x > −1 giving your answer in the form y = f (x) . (b) Determine the p
- June 2021, Further Pure 2 (FP2), Q8 (11 marks): (a) Show that the substitution v = y –2 transforms the differential equation d d e y x xy x y x x + = 6 3 0 2 3 > (I) into the differential equation d d e v x v
- January 2021, Further Pure 2 (FP2), Q4 (9 marks): (a) Show that the substitution y 2 = 1 z transforms the differential equation d d y x + 2y = 3xy 3 y ≠ 0 (I) into the differential equation d d z x − 4z = −6x (
- October 2020, Further Pure 2 (FP2), Q6 (8 marks): Obtain the general solution of the equation x2 d d y x + (x cot x + 2) xy = 4 sin x 0 < x < π Give your answer in the form y = f (x)
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