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A-LevelFurther MathematicsDifferential equations9231/12 · Oct/Nov 2019 · Q1114 Marks

Answer only one of the following two alternatives. EITHER It is given that w = cos y and tan y d²y/dx² + (dy/dx)² + 2 tan y dy/dx = 1 + e^(-2x) sec y.

  1. (i)Show that d²w/dx² + 2dw/dx + w = -e^(-2x).[4]
  2. (ii)Find the particular solution for y in terms of x, given that when x = 0, y = π/3 and dy/dx = 1/√3.[10]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.

  1. [B1]
  2. [B1]
  3. [M1] Uses substitution to obtain w-x equation, AG.
  4. [A1]
  5. [M1] Finds CF.
  6. [A1]
  7. [M1] Forms PI and differentiates.
  8. [A1]
  9. [A1] States general solution.
  10. [B1] Uses initial conditions to find constants.
  11. [M1] Differentiates general solution.
  12. [M1 A1] Substitutes initial conditions.
  13. [A1] States particular solution for y in terms of x.

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About this question

Topic
Differential equations, A-Level Further Mathematics (syllabus 9231). Structured question, 14 marks.
Source
A-Level Further Mathematics, Oct/Nov 2019 Paper 1 Variant 2, question 11.

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