$y = {x^2} + 2x + C:y' - 2x - 2 = 0$
$y = {x^2} + 2x + C:y' - 2x - 2 = 0$
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.: We have, $y = {x^2} + 2x + C$
…(1)
Differentiating (1) w.r.t. $x$,
we get
$y' = 2x + 2 \Rightarrow y' - 2x - 2 = 0$
Hence, $y = {x^2} + 2x + C$
is a solution of the given differential equation.
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