Q. 19
Solve: (x + y) (dx – dy) = dx + dy. [Hint: Substitute x + y = z after separating dx and dy].
Answer :
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) = ex-y
x + y = 1/c (ex-y)
x + y = d ex-y
where d = 1/c
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