For x ∈ R , let the function y ( x ) be the solution of the differential equation d y d x…
Mathematics · JEE Advanced · NTA Exams — Differential Equations
For x ∈ R, let the function y(x) be the solution of the differential equation
\(\frac{d y}{d x}+12 y=\cos \left(\frac{\pi}{12} x\right), y(0)=0 .\)
Then, which of the following statements is/are true?
\(\frac{d y}{d x}+12 y=\cos \left(\frac{\pi}{12} x\right), y(0)=0 .\)
Then, which of the following statements is/are true?
- y(x) is an increasing function
- y(x) is a decreasing function
- There exists a real number b such that the line
y = b intersects the curve y = y(x) at infinitely many points - y(x) is a periodic function
Answer
(C) There exists a real number b such that the line y = b intersects the curve y = y ( x ) at infinitely many points
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