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Vector Algebra

Question

In the following, verify that the given functions, (explicit or implicit) is a solution of the corresponding differential equation:
$straight y space equals space straight x squared plus 2 straight x plus straight C$ : $straight y apostrophe minus 2 straight x minus 2 space equals space 0$

Solution

y = x² + 2 x + C
∴ y' = 2 x + 2
⇒ y' – 2 x – 2 = 0
∴ y = x² + 2 x + C is a solution of y' – 2 x – 2 = 0