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Rates of change and differential equations — Question 18

QCAA 2023, Paper 1 · 6 marks

Q18 · 2023 · Technology-freeComplex unfamiliar6 marks

QUESTION 18 (6 marks)

A particular solution to the differential equation dydx=x(x2+1)tan⁡y,\frac{dy}{dx}=\frac{x}{(x^2+1)\tan y}, where x≥0x\ge0 and −π2<y≤0-\frac{\pi}{2}<y\le0, passes through the origin. Determine this solution in the form x=f(y)x=f(y). Leave your answer in simplified form.
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