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

y – cos y = x : (y sin y + cos y + x)y′ = y

It is given that y – cosy = x

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

⇒ y’(1 + siny) = 1

⇒ y’ =

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

LHS = (ysiny + cosy + x)y’

= y = RHS

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

11