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MathsJEE Main 28 Jan 2026, Shift 2·Q14·MCQ·Easy–moderate

Differential Equations · Linear first-order differential equation

Let y=y(x)y = y(x) be the solution of the differential equation xdydx−y=x2cot⁡xx\dfrac{dy}{dx} - y = x^2\cot x, x∈(0,π)x \in (0, \pi). If y(π2)=π2y\left(\dfrac{\pi}{2}\right) = \dfrac{\pi}{2}, then 6y(π6)−8y(π4)6y\left(\dfrac{\pi}{6}\right) - 8y\left(\dfrac{\pi}{4}\right) is equal to :
  1. (1)3π3\pi
  2. (2)−3π-3\pi
  3. (3)−π-\pi
  4. (4)π\pi

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