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MathsJEE Main 2 Apr 2026, Shift 1·Q17·MCQ·Easy–moderate

Differential Equations · Variable separable differential equations

If the curve y=f(x)y = f(x) passes through the point (1,e)(1, e) and satisfies the differential equation dy=y (2+log⁡ex) dxdy = y\,(2 + \log_e x)\,dx, x>0x > 0, then f(e)f(e) is equal to:
  1. (1)eee^{e}
  2. (2)ee2e^{e^2}
  3. (3)e2ee^{2e}
  4. (4)e2ee^{2^e}

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