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If y=y(x) is the solution curve of the differential equation dy dx+y tanx=x secx,0≤ x≤ π 3,y(0)=1, then y( π 6) is equal to

JEE Main 2023 — Mathematics Calculus

2023mcqeasy

If y=y(x)y=y(x)y=y(x) is the solution curve of the differential equation dydx+ytanx=xsecx,0≤x≤π3,y(0)=1\frac{dy}{dx}+y\mathrm{tan}x=x\mathrm{sec}x,0\leq x\leq \frac{\pi }{3},y(0)=1dxdy​+ytanx=xsecx,0≤x≤3π​,y(0)=1, then y(π6)y(\frac{\pi }{6})y(6π​) is equal to

Official previous-year question

Held on 1 Feb 2023 · Verified 6 Jul 2026.

Options

  1. A

    π12−32loge(2e3)\frac{\pi }{12}-\frac{\sqrt{3}}{2}{\mathrm{log}}_{e}(\frac{2}{e\sqrt{3}})12π​−23​​loge​(e3​2​)

  2. B

    π12+32loge(23e)\frac{\pi }{12}+\frac{\sqrt{3}}{2}{\mathrm{log}}_{e}(\frac{2\sqrt{3}}{e})12π​+23​​loge​(e23​​)

  3. C

    π12−32loge(23e)\frac{\pi }{12}-\frac{\sqrt{3}}{2}{\mathrm{log}}_{e}(\frac{2\sqrt{3}}{e})12π​−23​​loge​(e23​​)

  4. D

    π12+32loge(2e3)\frac{\pi }{12}+\frac{\sqrt{3}}{2}{\mathrm{log}}_{e}(\frac{2}{e\sqrt{3}})12π​+23​​loge​(e3​2​)

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