In each of the question verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:

It is given that

Now, differentiating both sides w.r.t. x, we get,

Now, Substituting the values of y’ in the given differential equations, we get,

LHS =

= x –x = 0 = RHS.

Therefore, the given function is the solution of the corresponding differential equation.

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