Verify that the function y = x^2 + 2x + C (explicit or implicit) … - Vidyadip

Question

Verify that the function $y = x^2 + 2x + C ($explicit or implicit$)$ is a solution of differential equation $y' - 2x - 2 = 0$

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Answer

Given: $y = x^2 + 2x + C ...(i)$
To prove: y is a solution of the differential equation $y' - 2x - 2 = 0 ...(ii)$
Proof:From, eq. $(i),$
$y' = 2x + 2$
$\text{L.H.S.}$ of eq. $(ii),$
$= y' - 2x - 2$
$= (2x + 2) - 2x - 2$
$= 2x + 2 - 2x - 2 = 0 = \text{}R.H.S.$
Hence, $y$ given by eq. $(i)$ is a solution of $y' - 2x - 2 = 0.$

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