Question

For $x \in R$, let the function $y ( x )$ be the solution of the differential equation $\frac{d y}{d x}+12 y=\cos \left(\frac{\pi}{12} x\right), y(0)=0 \text { }$.
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 $y =\beta$ intersects the curve $y = y ( x )$ at infinitely many points.
• D. $y ( x )$ is a periodic function.

Answer 1

Answer: (C)

There exists a real number $\beta$ such that the line $y =\beta$ intersects the curve $y = y ( x )$ at infinitely many points.

Answer 2

The correct option is (C): There exists a real number $\beta$ such that the line $y=\beta$ intersects the curve $y=y(x)$ at infinitely many points.