Answer :

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

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