Solve: (x + y) (dx – dy) = dx + dy. [Hint: Substitute x + y = z after separating dx and dy].

given: (x+y) (dx – dy) =dx+dy

To find: solution of given differential equation

Re-writing the given equation as

Assume x+y=z

Differentiating both sides wrt to x

Substituting this value in the given equation

Now integrating both sides

Formula:

Substituting z=x+y

x-y-ln(x + y)-c=0

ln(x + y) + ln c = x – y

ln c(x + y) = x – y

c (x + y) = e^x-y

x + y = 1/c (e^x-y)

x + y = d e^x-y

where d = 1/c