Solve the differential equation $y^{\prime}=\frac{x-y}{x+y}$

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Learn how to solve problems step by step online. Solve the differential equation y^'=(x-y)/(x+y). Rewrite the differential equation using Leibniz notation. We can identify that the differential equation \frac{dy}{dx}=\frac{x-y}{x+y} is homogeneous, since it is written in the standard form \frac{dy}{dx}=\frac{M(x,y)}{N(x,y)}, where M(x,y) and N(x,y) are the partial derivatives of a two-variable function f(x,y) and both are homogeneous functions of the same degree. Use the substitution: y=ux. Expand and simplify.