For \( x\in\mathbb{R} \), let the function \( y(x) \) be the solution of the differential equation \( \dfrac{dy}{dx}+12y=\cos\!\left(\dfrac{\pi}{12}x\right),\ y(0)=0 \).Then, which of the following statements is/are TRUE?
\( y(x) \) is an increasing function
\( y(x) \) is a decreasing function
There exists a real number \( \beta \) such that the line \( y=\beta \) intersects the curve \( y=y(x) \) at infinitely many points
\( y(x) \) is a periodic function
