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A-LevelFurther MathematicsDifferential equations9231/12 · Oct/Nov 2018 · Q48 Marks

Find the general solution of the differential equation d²x/dt² + 2dx/dt + x = 4 sin t.

  1. (i)Find the general solution of the differential equation d²x/dt² + 2dx/dt + x = 4 sin t.[7]
  2. (ii)State an approximate solution for large positive values of t.[1]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.

  1. [M1] Forms and solves auxiliary equation.
  2. [A1] States CF.
  3. [M1] Uses correct form of PI and differentiates twice.
  4. [A1]
  5. [M1] Compares coefficients and attempts to solve
  6. [A1]
  7. [A1FT] States general solution. FT on correct form only
  8. [B1FT]

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About this question

Topic
Differential equations, A-Level Further Mathematics (syllabus 9231). Structured question, 8 marks.
Source
A-Level Further Mathematics, Oct/Nov 2018 Paper 1 Variant 2, question 4.

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