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Differential Equations question

2024 · 6 Apr · Shift 1 · Q40

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JEE Main
Mathematics
Differential Equations
2024 · 6 Apr · Shift 1 · Q40

Differential Equations question

2024 · 6 Apr · Shift 1 · Q40

JEE MainMathematicsDifferential EquationsMCQ+4 / −1

Let

y=y(x)

be the solution of the differential equation

\left(2 x \log _e x\right) \frac{d y}{d x}+2 y=\frac{3}{x} \log _e x, x\gt 0

and

y\left(e^{-1}\right)=0

. Then,

y(e)

is equal to

A
$-\frac{3}{\mathrm{e}}$
B
$-\frac{3}{2 \mathrm{e}}$
C
$-\frac{2}{3 \mathrm{e}}$
D
$-\frac{2}{\mathrm{e}}$

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