The D.E whose solution is $y = c x + c - c^{2}$ is

{y_{1}}^{2} + y = (x + 1) y_{1}

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{y_{1}}^{2} + y_{1} = (x + 1) y

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{y_{1}}^{2} + y = (x - 1) y_{1}

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y = x y + y_{1} - {y_{1}}^{2}

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Solution

The correct option is A ${y_{1}}^{2} + y = (x + 1) y_{1}$
$y = c x + c - c^{2}$
$\Rightarrow y_{1} = c$
$\Rightarrow y = x y_{1} + y_{1} - y_{1}^{2}$
$y_{1}^{2} + y - y_{1} (1 + x) = 0$

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