Test that the function  y = x² + 2x +C  is the solution of the differential equation y'- 2x -2 = 0-

yes

we have y = x² + 2x +C

differentiating both side with respect to x, we get:

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 given differential equation.