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

Question

Which of the following is true for y(x) that satisfies the differential equation

${{dy} \over {dx}}$ = xy $-$ 1 + x $-$ y; y(0) = 0 :

y(1) = 1

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

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

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

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