🛠️ JEE➗ Maths

Let \(x=x(y)\) be the solution of the differential equation \(y^2 d x+\left(x-\frac{1}{y}\right) d y=0\). If \(x(1)=1,\)…

Q1

Let \(x=x(y)\) be the solution of the differential equation \(y^2 d x+\left(x-\frac{1}{y}\right) d y=0\). If \(x(1)=1,\) then \(x\left(\frac{1}{2}\right)\) is:

[JEE Main 2025, 22 Jan (Shift 1)]

a

\(\frac{1}{2}+\mathrm{e}\)

b

\(\frac{3}{2}+\mathrm{e}\)

c

\(3-e\)

d

\(3+e\)

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