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Which of the following is true for \(y(x)\) that satisfies the differential equation \(\frac{dy}{dx}=xy-1+x-y;y(0)=0\) :…

Q1

Which of the following is true for \(y(x)\) that satisfies the differential equation \(\frac{dy}{dx}=xy-1+x-y;y(0)=0\) :

[JEE Main 2021, 17 Mar (Shift 1)]

a

\(y(1)={e}^{\frac{1}{2}}-1\)

b

\(y(1)=1\)

c

\(y(1)={e}^{\frac{1}{2}}-{e}^{-\frac{1}{2}}\)

d

\(y(1)={e}^{-\frac{1}{2}}-1\)

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