2025 RVHS Promo Q9

2025 RVHS Promo Q9

Junior College 1
10 marks
  1. Find \(\int e^{2x} \cos x\, dx\).[4]
  2. Given that \(y=-1\) when \(x=0\), solve the differential equation\n\(\ne^{-2x}\frac{dy}{dx}=5y\cos x+2y,\n\)\nexpressing \(y\) in terms of \(x\).[6]

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Answer:\(\int e^{2x}\cos x\,dx=\dfrac15e^{2x}(2\cos x+\sin x)+C\); \(y=-e^{e^{2x}(2\cos x+\sin x+1)-3}\)

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