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For x belonging to the set of real numbers, consider the function y(x) that satisfies the differential equation dy/dx + 12y = cos(π/12 * x), with the initial condition y(0) = 0. Which of the following statements is/are correct?
- y(x) increases as x increases.
- y(x) decreases as x increases.
- There exists a real constant β such that the line y = β meets the curve y = y(x) at infinitely many points.
- y(x) is a periodic function.
Correct answer: There exists a real constant β such that the line y = β meets the curve y = y(x) at infinitely many points.
Solution
The differential equation solution shows that y(x) oscillates and approaches a steady-state value. The line y = β intersects the periodic oscillations of y(x) infinitely many times, confirming the correct statement.
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