8. In each of the Exercises 1 to 10 verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:
Given,
Now, differentiating both sides w.r.t. x,
y' + siny.y' = 1
y'(1 + siny) = 1
Substituting the values of y and y' in LHS,
= (x + cosy) = y = RHS
Therefore, the given function is a solution of the corresponding differential equation.