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MathsJEE Main 2 Apr 2026, Shift 1·Q20·MCQ·Easy–moderate

Differential Equations · Exact differential equations

Let y=y(x)y = y(x) be the solution curve of the differential equation (1+sin⁡x)dydx+(y+1)cos⁡x=0(1 + \sin x)\dfrac{dy}{dx} + (y + 1)\cos x = 0, y(0)=0y(0) = 0. If the curve y=y(x)y = y(x) passes through the point (α,−12)\left(\alpha, \dfrac{-1}{2}\right), then a value of α\alpha is:
  1. (1)π6\dfrac{\pi}{6}
  2. (2)π4\dfrac{\pi}{4}
  3. (3)π3\dfrac{\pi}{3}
  4. (4)π2\dfrac{\pi}{2}

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