A curve is such that \(\dfrac{\mathrm{d}^2y}{\mathrm{d}x^2}=\cos\left(4x-\dfrac\pi4\right)\). Given that \(\dfrac{\mathrm{d}y}{\mathrm{d}x}=\dfrac34\) at the point \(\left(\dfrac{3\pi}{16},\dfrac\pi4\right)\) on the curve, find the equation of the curve.[7]
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