Given cos x (1+cos y) dx – sin y (1+sin x) dy = 0
Let 1+cos y = t and 1+sin x = u
On differentiating both equations, we get
-sin y dy = dt and cos x dx = du
Substitute this in the first equation
t du + u dt = 0
-log u = log t + C
log u + log t = C
log ut = C
ut = C
(1+sin x)(1+cos y) = C
Conclusion: Therefore, (1+sin x)(1+cos y) = C is the solution of cos x (1+cos y) dx – sin y (1+sin x) dy = 0