Q. 9

# Solve the following differential equations:(x + y)(dx–dy) = dx + dy

Given Differential equation is:

(x + y)(dx–dy) = dx + dy

(x + y)dx –(x + y)dy = dx + dy

(x + y–1)dx = (x + y + 1)dy

……(1)

Let us assume z = x + y

Differentiating w.r.t x on both sides we get,

……(2)

Substituting (2) in (1) we get,

Bringing like variables on same side(i.e., variable seperable technique) we get,

Integrating on both sides we get,

We know that:

(1) ∫ adx = ax + C

(2)

Since z = x + y we substitute this,

x + y + log(x + y) = 2x + C

y + log(x + y) = x + C

The solution for the given Differential equation is y + log(x + y) = x + C.

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