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

Explanation

`y=x^{2}+2 x+C`


Differentiating the equation with respect to x,


`y^{prime}=frac{d}{d x}(x^{2}+2 x+C}`


`Rightarrow y^{prime}=2 x+2`


Substitute the value of y^{prime} in the differential equation,


`y^{prime}-2 x-2`


`=2 x+2-2 x-2`


`=0`


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