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.

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