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

**Calculus**Level 4

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 \(x=0\).

**Input the value of \(p\) as your answer.**

###### 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.

###### This is part of the set OCR A Level Problems.

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