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Question
Solve : cos x(1 + cosy) dx – sin y(1 + sinx) dy = 0
Solution
cos x(1 + cos y) dx = sin y(1 + sin x) dy
`cosx/((1 + sin x)) "d"x = siny/((1 + cos y)) "d"y`
Integrating on both sides
`int cosx/((1 + sin x)) "d"x = int siny/((1 + cos y)) "d"y`
`int cosx/((1 + sin x)) "d"x = - int (-siny)/((1 + cos y)) "d"y`
`log (1 + sin x) = - log (1 + cos y) + log "c"`
`log(1 + sin x) = log ("c"/((1 + cos y)))`
`(1 + sin x) = "c"/((1 + cos y))`
⇒ (1 + sin x)(1 + cos y) = c
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