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Rates of change and differential equations — Question 3

QCAA 2022, Paper 2 · 1 mark

Q3 · 2022 · Technology-activeSimple familiar1 mark

QUESTION 3

Determine the solution of the differential equation dydx=sin⁡(2x)cos⁡(2x)\dfrac{dy}{dx}=\dfrac{\sin(2x)}{\cos(2x)} given y=0y=0 when x=π5x=\dfrac{\pi}{5}.
(A)
y=−2ln⁡∣cos⁡(2x)∣−2.35y=-2\ln|\cos(2x)|-2.35
(B)
y=−2ln⁡∣cos⁡(2x)∣+2.35y=-2\ln|\cos(2x)|+2.35
(C)
y=−12ln⁡∣cos⁡(2x)∣−0.59y=-\dfrac12\ln|\cos(2x)|-0.59
(D)
y=−12ln⁡∣cos⁡(2x)∣+0.59y=-\dfrac12\ln|\cos(2x)|+0.59
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