Question

Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:

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

Answer 1

y - cos y = 3x

y’ + sin y : y’ = 1

y (1 + sin y) = 1

⇒ y’ = `1/(1 + sin y)`

Putting the values ​​of y' and y in the differential equation (y sin y + cos y + x) y’ = y

L.H.S. {(x + cos y) sin y + cosy + x}·  `1/(1 + sin y)`

⇒ x + cos y = y

R.H.S. Hence, the given function y - cos y = 3x is a solution of the given differential equation.