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MCQMediumJEE Main 2023 · 15 April, Shift 1Linear Differential Equations

Mathematics Question from JEE Main 2023 · 15 April, Shift 1

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

2(y+2)log⁡e(y+2) dx+(x+4−2log⁡e(y+2)) dy=0,y>−1,2(y+2)\log_e(y+2)\,dx+(x+4-2\log_e(y+2))\,dy=0,\quad y>-1,

with x(e4−2)=1x(e^{4}-2)=1. Then x(e9−2)x(e^{9}-2) is equal to

  • A

    33

  • B

    103\dfrac{10}{3}

  • C

    49\dfrac{4}{9}

  • D

    329\dfrac{32}{9}

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