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**1. The problem statement, all variables and given/known data**

Solve the following initial value problem,

y' = (x-y)/(x+y), y(1) = 1

**2. Relevant equations**

**3. The attempt at a solution**

dy/dx = (x-y)/(x+y)

dy/dx * (x+y) = x-y

(x+y)dy = (x-y)dx

∫(x+y)dy = ∫(x-y)dx

xy + y^(2)/2 = x^(2)/2 - xy + C

2xy + y^2 = x^2 - 2xy + C

y^2 + 4xy - x^2 = C

Sub in x=1, y=1

1 + 4 - 1 = C = 4

Soln: 2xy + y^2 = x^2 - 2xy + 4