OCR A Level: Further Pure 3 - Differential Equations [January 2010 Q6]

The variables $x$ and $y$ satisfy the differential equation $\dfrac{\text{d}^2y}{\text{d}x^2} +16y = 8\cos 4x.$ $(\text{i})$ Find the complementary function of the differential equation.

$(\text{ii})$ Given that there is a particular integral of the form $y=px \sin 4x$ , where $p$ is a constant, find the general solution of the equation.

$(\text{iii})$ Find the solution of the equation for which $y=2$ and $\dfrac{\text{d}y}{\text{d}x}=0$ when $x=0$ .

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Input the value of $p$ as your answer.

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There are 2 marks available for part (i), 6 marks for part (ii) and 4 marks for part (iii).

In total, this question is worth 16.7% of all available marks in the paper.

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This is part of the set OCR A Level Problems .