Question

The solution of the DE `cos x (1 + cosy )dx - sin y (1+ sin x ) dy=0 ` is
A. `1 + sin x cos y = C `
B. ` (1 + sin x ) (1 + cos y ) = C `
C. `sinx cos y + cos x = C `
D. none of these

Answer 1

Correct Answer - B
`int (cos x )/((1 +sin x )) dx - int (sin y )/((1+ cos y )) dy = log C`
` rArr log (1 + sin x ) + log (1 + cos y ) = log C rArr (1 + sin x ) (1 + cos y ) =C`.