A-LevelMathematicsDifferential equations9709/33 · Oct/Nov 2023 · Q87 Marks

The variables x and y satisfy the differential equation e^(4x) dy/dx = cos² 3y. It is given that y = 0 when x = 2. Solve the differential equation, obtaining an expression for y in terms of x.

The variables x and y satisfy the differential equation e^(4x) dy/dx = cos² 3y. It is given that y = 0 when x = 2. Solve the differential equation, obtaining an expression for y in terms of x.[7]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2023). The mark or mark type is shown in brackets.

[B1] Separate variables correctly and reach sec² 3y dy = e⁻⁴x dx.
[B1] Obtain term -1/4 e⁻⁴x.
[M1] Obtain only a term of the form a tan 3y.
[A1] Obtain term 1/3 tan 3y.
[M1] Use x = 2, y = 0 to evaluate a constant or as limits in a solution containing terms of the form a tan by and ce^(±4x).
[A1] Obtain correct answer in any form, e.g. 1/3 tan 3y = -1/4 e⁻⁴x + 1/4 e⁻⁸ or 1/3 tan 3y = -1/4 e⁻⁴x + 8.39 × 10⁻⁵.
[A1] Obtain final answer y = 1/3 tan⁻¹ (3/4 e⁻⁸ - 3/4 e⁻⁴x). ISW. OE e.g. y = 1/3 tan⁻¹ (2.52×10⁻⁴ - 3/4 e⁻⁴x).

On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.

Topic: Differential equations, A-Level Mathematics (syllabus 9709). Structured question, 7 marks.
Source: A-Level Mathematics, Oct/Nov 2023 Paper 3 Variant 3, question 8.

Questions and mark schemes are from past examination papers and remain the copyright of the exam board. How Oracle Prep builds its content