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MathsJEE Main 21 Jan 2026, Shift 1·Q8·MCQ·Moderate

Differential Equations · Linear differential equations

Let y=y(x)y = y(x) be the solution curve of the differential equation (1+x2) dy+(y−tan⁡−1x) dx=0(1 + x^2)\,dy + (y - \tan^{-1}x)\,dx = 0, y(0)=1y(0) = 1. Then the value of y(1)y(1) is:
  1. (1)2eπ4+π4−1\dfrac{2}{e^{\frac{\pi}{4}}} + \dfrac{\pi}{4} - 1
  2. (2)2eπ4−π4−1\dfrac{2}{e^{\frac{\pi}{4}}} - \dfrac{\pi}{4} - 1
  3. (3)4eπ4+π2−1\dfrac{4}{e^{\frac{\pi}{4}}} + \dfrac{\pi}{2} - 1
  4. (4)4eπ4−π2−1\dfrac{4}{e^{\frac{\pi}{4}}} - \dfrac{\pi}{2} - 1

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