In each of the verify that the given function (explicit or implic… - Vidyadip

Question

In each of the verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
$\text{y} = \text{x}^2 + 2\text{x} +\text{C}\ :\ \text{y}' – 2\text{x} – 2 = 0$

✓

Answer

Given: y = x² + 2x + C .....(i)
To prove: y is a solution of the differential equation y' - 2x - 2 = 0 .....(ii)
Proof: From eq. y' = 2x + 2
$\therefore$ L.H.S. of eq. (ii), y' - 2x - 2 = (2x + 2) - 2x - 2
= 2x + 2 - 2x - 2 = 0 = R.H.S.
Hence, y given by eq. (i) is a solution of y' - 2x - 2 = 0.

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