3.83: Second-order differential equation of a curve

A curve is such that $\dfrac{\mathrm{d}^{2}y}{\mathrm{d}x^{2}} = \sin\left(6x - \dfrac{\pi}{2}\right)$. Given that $\dfrac{\mathrm{d}y}{\mathrm{d}x} = \dfrac{1}{2}$ at the point $\left(\dfrac{\pi}{4}, \dfrac{13\pi}{12}\right)$ on the curve, find the equation of the curve.