4PM1/02 Jan 2020, Question 8: The Product and Quotient Rules
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2 · Calculator · 8 marks
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The question, in short
For y = e^(3x) sin 2x, differentiate twice and confirm that the second derivative minus 6 times the first derivative plus 13y equals zero.
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Solution · 8 marks
- 1dy/dx = 2e^(3x) cos 2x + 3e^(3x) sin 2x
- 2d²y/dx² = (−4e^(3x) sin 2x + 6e^(3x) cos 2x) + (6e^(3x) cos 2x + 9e^(3x) sin 2x)
- 3d²y/dx² = 12e^(3x) cos 2x + 5e^(3x) sin 2x
- 4−6 dy/dx = −12e^(3x) cos 2x − 18e^(3x) sin 2x
- 5Sum with 13y = 13e^(3x) sin 2x:
- 6cos terms: 12 − 12 = 0; sin terms: 5 − 18 + 13 = 0, so the result is 0
Answerd²y/dx² − 6 dy/dx + 13y = 0 shown
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