Differential equations: past paper questions

Real questions on differential equations

The newest 20 of 52 written questions. Open one to see it on the real paper.

1. 9709/32 · May/June 2026 · Q10b[7]
   (b) The variables $x$ and $y$ satisfy the differential equation $(x-1)(2x-6)\frac{\mathrm{d}y}{\mathrm{d}x}=\frac{x+3}{\ln (2y)}$. It is given that $y=1$ when $x=4$. Solve the differential equation to obtain an equation in $x$ and $y$.See it on the paper →
2. 9709/22 · October/November 2025 · Q5a[5]

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3. 9709/32 · May/June 2025 · Q8[7]

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4. 9709/33 · May/June 2025 · Q5a[4]

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5. 9709/33 · May/June 2025 · Q10a[8]

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6. 9709/33 · May/June 2025 · Q10b[2]

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7. 9709/22 · February/March 2025 · Q2[3]

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8. 9709/32 · February/March 2025 · Q6[7]

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9. 9709/42 · February/March 2025 · Q7a[6]

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10. 9709/42 · February/March 2025 · Q7b[5]

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11. 9709/43 · October/November 2024 · Q6a[1]

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12. 9709/43 · October/November 2024 · Q6b[3]

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13. 9709/43 · October/November 2024 · Q6c[2]

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14. 9709/43 · October/November 2024 · Q6d[4]

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15. 9709/31 · May/June 2024 · Q10a[3]

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16. 9709/31 · May/June 2024 · Q11a[2]

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17. 9709/31 · May/June 2024 · Q11b[9]

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18. 9709/32 · May/June 2024 · Q10b[8]

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19. 9709/33 · May/June 2024 · Q9a[5]

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20. 9709/33 · May/June 2024 · Q9b[6]

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What examiners said

The majority of candidates were able to differentiate and integrate correctly and go on to use the given information at t = 1 to produce two correct equations. The majority then solved these simultaneous equations correctly to show the given values. However, a minority of candidates showed no working and just stated the given values and hence did not earn full credit.

— Examiner report, February/March 2025, 9709/42 Q7(a) (Cambridge)

The majority of candidates correctly found the times at which a = 0 and v = 0 and used these correctly to find the required distance. The main error seen by examiners was to find the difference between the two times found and use this to find a distance.

— Examiner report, February/March 2025, 9709/42 Q7(b) (Cambridge)

This was a straight-forward question for many candidates. Some candidates did not take sufficient care in placing the minus sign, leading to ambiguous or incorrect answers. Some candidates did not use the notation for derivatives correctly.

— Examiner report, May/June 2023, 9709/32 Q7(a) (Cambridge)