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Mathematics Question on Differential equations

General Solution of the differential equation:
cos x(1+cos y)dx−sin y(1+sin x)dy=0cos\,x(1+cos\,y)dx-sin\,y(1+sin\,x)dy=0 is:

A

(1+cos x)(1+sin y)(1+cos\,x)(1+sin\,y)= c

B

1+sin x+cos y=c1+sin\,x+cos\,y=c

C

(1+sin x)(1+cos y)=c(1+sin\,x)(1+cos\,y)=c

D

1+sin x.cos y=c1+sin\,x.cos\,y=c

Answer

(1+sin x)(1+cos y)=c(1+sin\,x)(1+cos\,y)=c

Explanation

Solution

The correct option is (C): (1+sin x)(1+cos y)=c(1+sin\,x)(1+cos\,y)=c