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MCQMediumJEE Main 2024 · 27 January, Shift 2Separation of Variables

Mathematics Question from JEE Main 2024 · 27 January, Shift 2

If y=y(x)y = y(x) is the solution curve of the differential equation (x2−4) dy−(y2−3y) dx=0(x^2 - 4) \, dy - (y^2 - 3y) \, dx = 0, x>2x > 2, y(4)=32y(4) = \frac{3}{2}, and the slope of the curve is never zero, then y(10)y(10) equals:

  • A

    31+81/4\frac{3}{1 + 8^{1/4}}

  • B

    31+22\frac{3}{1 + 2\sqrt{2}}

  • C

    31−22\frac{3}{1 - 2\sqrt{2}}

  • D

    31−81/4\frac{3}{1 - 8^{1/4}}

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