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 (\frac{\pi}{12} x), y(0)=0 Then, which of the following statements is/are TRUE? [JEE Adv 2022 P2]

Correct Answer is : There exists a real number β such that the line y=β intersects the curve y=y(x) at infinitely many points

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

Differential Equations

Section: Mathematics

Question : 6 of 23

Marks: +1, -0

For x∈ℝ, let the function y(x) be the solution of the differential equation
‌

+12y=cos(‌

x),‌‌y(0)=0
Then, which of the following statements is/are TRUE?

[JEE Adv 2022 P2]

y(x) is an increasing function
y(x) is a decreasing function
There exists a real number β such that the line y=β‌‌ intersects the curve y=y(x) at
infinitely many points
y(x) is a periodic function

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