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MCQMediumJEE Main 2023 · 30 January, Shift 1Linear Differential Equations

Mathematics Question from JEE Main 2023 · 30 January, Shift 1

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

dydx−3x5tan⁡−1(x3)(1+x6)3/2 y=2xexp⁡ ⁣(x3−tan⁡−1(x3)1+x6)\frac{dy}{dx} - \frac{3x^5 \tan^{-1}(x^3)}{(1+x^6)^{3/2}}\, y = 2x \exp\!\left(\frac{x^3 - \tan^{-1}(x^3)}{\sqrt{1+x^6}}\right)

pass through the origin. Then y(1)y(1) is equal to:

  • A

    exp⁡(4−π42)\exp\left(\frac{4 - \pi}{4\sqrt{2}}\right)

  • B

    exp⁡(π−442)\exp\left(\frac{\pi - 4}{4\sqrt{2}}\right)

  • C

    exp⁡(1−π42)\exp\left(\frac{1 - \pi}{4\sqrt{2}}\right)

  • D

    exp⁡(4+π42)\exp\left(\frac{4 + \pi}{4\sqrt{2}}\right)

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