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MCQMediumJEE Main 2023 · 25 January, Shift 1Linear Differential Equations

Mathematics Question from JEE Main 2023 · 25 January, Shift 1

Let y=y(x)y = y(x) be the solution curve of the differential equation

dydx=yx(1+xy2(1+log⁡x)),x>0, y(1)=3.\frac{dy}{dx} = \frac{y}{x}(1 + xy^2(1 + \log x)), \quad x > 0, \, y(1) = 3.

Then y2(x)9\frac{y^2(x)}{9} is equal to:

  • A

    x25−2x3(2+log⁡x3)\frac{x^2}{5 - 2x^3(2 + \log x^3)}

  • B

    x22x3(2+log⁡x3)−3\frac{x^2}{2x^3(2 + \log x^3) - 3}

  • C

    x23x3(1+log⁡x2)−2\frac{x^2}{3x^3(1 + \log x^2) - 2}

  • D

    x27−3x3(2+log⁡x2)\frac{x^2}{7 - 3x^3(2 + \log x^2)}

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