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Grouping the terms of the differential equation
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$y\cdot dy=\frac{y^2-xy+x^2}{x}dx$
Learn how to solve differential equations problems step by step online. Solve the differential equation xydy=(y^2-xyx^2)dx. Grouping the terms of the differential equation. Divide both sides of the equation by d. Rewrite the differential equation. We can identify that the differential equation \frac{dy}{dx}=\frac{y^2-xy+x^2}{xy} 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.