Find the general solution of each of the following differential equations:
`cosx(1+cosy)dx -siny (1+sinx)dy =0`

Options

A. `(1+sin x)(1+cosy) =C`
B. `(1-sin x)(1+cosy) =C`
C. `(1-sin x)(1-cosy) =C`
D. `(1+2sin x)(3+cosy) =C`

Answer

A

Explanation

`int (cosx)/((1+cosx))dx + int (-siny)/((1+cosy))dy = log |C_(1)|`
`rArr log |1+sinx|+log|1+cosy|=log |C_(1)|rArr log |(1+sinx)(1+cosy)=log |C_(1)|`
`rArr |(1+sinx) (1+cosy)|=C_(1) rArr (1+sinx)(1+cosy) = pm C_(1) = C.`