Mathematics

Problem

For

x \in \mathbb{R}

, let the function

y(x)

be the solution of the differential equation

\frac{dy}{dx} + 12y = \cos\left(\frac{\pi}{12}x\right)

y(0) = 0

. Then, which of the following statements is/are TRUE? [JEE-Advanced 2022] (A)

y(x)

is an increasing function (B)

y(x)

is a decreasing function (C) There exists a real number

\beta

such that the line

y = \beta

intersects the curve

y = y(x)

at infinitely many points (D)

y(x)

is a periodic function