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Differential Equations question

2025 · 22 Jan · Shift 1 · Q34

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JEE Main
Mathematics
Differential Equations
2025 · 22 Jan · Shift 1 · Q34

Differential Equations question

2025 · 22 Jan · Shift 1 · Q34

JEE MainMathematicsDifferential EquationsMCQ+4 / −1

Let

x=x(y)

be the solution of the differential equation

y^2 \mathrm{~d} x+\left(x-\frac{1}{y}\right) \mathrm{d} y=0

. If

x(1)=1

, then

x\left(\frac{1}{2}\right)

is :

A
$\frac{3}{2}+\mathrm{e}$
B
$\frac{1}{2}+\mathrm{e}$
C
$3+e$
D
$3-e$

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