Question

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

Answer 1

$y=x^2+2x+C$
Differentiating both sides of this equation with respect to x, we get:
$y' = \frac{d}{dx}\big(x^2+2x+C\big)$
$\Rightarrow y'=2x+2$
Substituting the value of y' in the given differential equation, we get:
L.H.S = $y'-2x-2=2x+2-2x-2=0=$ R.H.S.
Hence, the given function is the solution of the corresponding differential equation