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MCQMediumJEE Main 2023 · 6 April, Shift 2Separation of Variables

Mathematics Question from JEE Main 2023 · 6 April, Shift 2

If the solution curve f(x,y)=0f(x, y) = 0 of the differential equation

(1+log⁡ex)dxdy−xlog⁡ex=ey,x>0(1 + \log_e x)\frac{dx}{dy} - x\log_e x = e^{y},\qquad x > 0

passes through the points (1,0)(1, 0) and (α,2)(\alpha, 2), then αα\alpha^{\alpha} is equal to:

  • A

    e2e2e^{\sqrt{2}e^2}

  • B

    e2e2e^{2e^{\sqrt{2}}}

  • C

    ee2e^{e^2}

  • D

    e2e2e^{2e^2}

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