Paper 2 · Differential equations: separable, exponential decay

Find the equation of the curve which satisfies $\dfrac{dy}{dx}=-\dfrac{x}{y}$ and passes through $(-4,3)$ .

Model answer

x^2+y^2=25

Also accepted: x^2 + y^2 = 25

Explanation: Separating variables:

y\,dy=-x\,dx\Rightarrow x^2+y^2=2C

. Using

(-4,3)

16+9=25=2C

, so

x^2+y^2=25

Derived from ZIMSEC Pure Mathematics Paper 2, November 2025, Q7

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