4PM1/02R Jun 2020, Question 9: The Product and Quotient Rules
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2R · Calculator · 8 marks
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The question, in short
For x = e^(−t) sin 2t, verify by differentiation that the second derivative plus twice the first derivative plus 5x equals zero.
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Solution · 8 marks
- 1dx/dt = −e^(−t) sin 2t + 2e^(−t) cos 2t = 2e^(−t) cos 2t − x
- 2d²x/dt² = −2e^(−t) cos 2t − 4e^(−t) sin 2t − dx/dt
- 32e^(−t) cos 2t = dx/dt + x and 4e^(−t) sin 2t = 4x
- 4d²x/dt² = −(dx/dt + x) − 4x − dx/dt = −5x − 2 dx/dt
- 5Hence d²x/dt² + 2 dx/dt + 5x = 0
Answerd²x/dt² + 2 dx/dt + 5x = 0 shown
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