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

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Best answer

Given: (x+y) (dx – dy) =dx+dy

To find: solution of given differential equation

Re-writing the given equation as

Substituting this value in the given equation

Now integrating both sides

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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