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Differential Equations question

2022 · Shift 2 · Q32

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JEE Advanced
Mathematics
Differential Equations
2022 · Shift 2 · Q32

Differential Equations question

2022 · Shift 2 · Q32

JEE AdvancedMathematicsDifferential EquationsMultiple correct+4 / −2

For

x \in \mathbb{R}

, let the function

y(x)

be the solution of the differential equation

\frac{d y}{d x}+12 y=\cos \left(\frac{\pi}{12} x\right), \quad y(0)=0

Then, which of the following statements is/are TRUE ?

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 $y=\beta \quad$ intersects the curve $y=y(x)$ at infinitely many points
D
$y(x)$ is a periodic function

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