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MCQMediumJEE Main 2023 · 12 April, Shift 1Linear Differential Equations

Mathematics Question from JEE Main 2023 · 12 April, Shift 1

Let y=y(x), y>0y = y(x), \, y > 0, be a solution curve of the differential equation (1+x2) dy=y(x−y) dx(1 + x^2) \, dy = y(x - y) \, dx. If y(0)=1y(0) = 1 and y(22)=βy(2\sqrt{2}) = \beta, then:

  • A

    e3β−1=e(3+22)e^{3\beta^{-1}} = e\left(3 + 2\sqrt{2}\right)

  • B

    eβ−1=e−2(5+2)e^{\beta^{-1}} = e^{-2}\left(5 + \sqrt{2}\right)

  • C

    eβ−1=e−2(3+22)e^{\beta^{-1}} = e^{-2}\left(3 + 2\sqrt{2}\right)

  • D

    e3β−1=e(5+2)e^{3\beta^{-1}} = e\left(5 + \sqrt{2}\right)

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