For x R , let the function y(x) be the solution of the differential equation dy dx + 12y = ( 12 x ), y(0) = 0. Then, which of the following statements is/are TRUE ?

JEE Advanced 2022 Mathematics question

For , let the function be the solution of the differential equation

+ 12y = (x), y(0) = 0.

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

(A) is an increasing function
(B) is a decreasing function
(C)There exists a real number such that the line intersects the curve at infinitely many pointsCorrect
(D) is a periodic function

Answer: (C)

Solution

With , the solution is . As the exponential term dies out and approaches a sinusoid of period 24, so keeps rising and falling: it is neither increasing

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Question ID VK-034021