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Differential Equations question

2023 · 15 Apr · Shift 1 · Q24

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JEE Main
Mathematics
Differential Equations
2023 · 15 Apr · Shift 1 · Q24

Differential Equations question

2023 · 15 Apr · Shift 1 · Q24

JEE MainMathematicsDifferential EquationsMCQ+4 / −1

Let

x=x(y)

be the solution of the differential equation

2(y+2) \log _{e}(y+2) d x+\left(x+4-2 \log _{e}(y+2)\right) d y=0, y\gt -1

with

x\left(e^{4}-2\right)=1

. Then

x\left(e^{9}-2\right)

is equal to :

A
$\frac{4}{9}$
B
$\frac{32}{9}$
C
$\frac{10}{3}$
D
3

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