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DE of y = e^x (A cos x + B sin x)

The same question, asked 2 times: 14 May 2024 S1, 25 Apr 2025 S1. Every wording below, oldest first.

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  1. Question 1

    14 May 2024 S1

    142
    The differential equation of y=ex(acos⁡x+bsin⁡x)y=e^x(a\cos x+b\sin x) is

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  2. Question 2

    25 Apr 2025 S1

    138
    y=ex( Acosx+Bsinx)y=e^{x}(\text{ }Acosx+ Bsinx) is the solution of the differential equation

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