The solution of differential edquation `(dy)/(dx) +1 = cosec (x+y)` is

Options

A. `cos(x+y)+x=C`
B. `cos(x+y)=C`
C. `sin(x+y)+x=C`
D. `sin(x+y)+sin(x+y)=C`

Answer

b

Explanation

Given `(dy)/(dx) +1 = " cosec" (x+y)`
Put ` x+y = t`
` rArr 1+ (dy)/(dx) = (dt)/(dx)`
` :. (dt)/("cosec t ") = dx `
` rArr int sin t dt = int dx `
` rArr cos ( x+y) +x = C`