Question

Solve: (x + y)(dx – dy) = (dx + dy).

Answer 1

The given differential equation is

(x + y)(dx – dy) = (dx + dy)

(x + y) d(x – y) = d(x + y)

d(x - y) = d(x + y)/(x + y)

Integrating, we get 

(x – y) = log|(x + y)|

which is the required solution.