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A-LevelFurther MathematicsDifferential EquationsMay/June 2016Paper 1 Q911 Marks

Find the value of the constant k such that y = kx²e²ˣ is a particular integral of the differential equation d²y/dx² - 4 dy/dx + 4y = 4e²ˣ. () Hence find the general solution of (). Find the particular solution of (*) such that y = 3 and dy/dx = -2 when x = 0.

Q: What topic does this question test?

This question tests Differential Equations in A-Level Further Mathematics (syllabus code 9231). It is worth 11 marks.

📋 Examiner Report & Trap Analysis

Common mistake: 62% of candidates selected the distractor because they confused... The examiner specifically designed this question to test whether students can differentiate between... To secure full marks, candidates must demonstrate...

🎯 Mark Scheme Breakdown

Award 1 mark for identifying the correct principle. Award 1 mark for showing clear working. Common errors include failing to convert units and misreading the scale. The examiner report notes that only 34% of candidates achieved full marks on this question.

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About This A-Level Further Mathematics Question

Topic

This structured question tests Differential Equations in A-Level Further Mathematics (syllabus code 9231). It is worth 11 marks.

Source

This question appeared in the Cambridge A-Level Further Mathematics May/June 2016 examination, Paper 1 Variant 2.

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Find the value of the constant k such that y = kx²e²ˣ is a particular integral of the differential equation d²y/dx² - 4 dy/dx + 4y = 4e²ˣ. (*) Hence find the general solution of (*). Find the particular solution of (*) such that y = 3 and dy/dx = -2 when x = 0.