🛠️ JEE➗ Maths

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

Q1

Let \(y=y(x), y>0\), be a solution curve of the differential equation \(\left(1+x^2\right) d y=y(x-y) d x\). If \(y(0)=1\) and \(y(2 \sqrt{2})=\beta\), then

[JEE Main 2023, 12 Apr (Shift 1)]

a

\(e^{3 \beta^{-1}}=e(3+2 \sqrt{2})\)

b

\(e^{\beta^{-1}}=e^{-2}(5+\sqrt{2})\)

c

\(e^{\beta^{-1}}=e^{-2}(3+2 \sqrt{2})\)

d

\(e^{3 \beta^{-1}}=e(5+\sqrt{2})\)

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