Differentiating both sides of eq. (i) w.r.t 
we have
……….(iii)
Putting the value of 
from eq. (i) and value of 
from eq. (iii) in L.H.S. of eq. (ii),
= R.H.S. of (ii)
Hence, Function given by eq. (i) is a solution of 
.
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
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