** Final answer to the problem

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** Step-by-step Solution **

** How should I solve this problem?

- Choose an option
- Exact Differential Equation
- Linear Differential Equation
- Separable Differential Equation
- Homogeneous Differential Equation
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
- Integrate by substitution
- Integrate by parts
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We can identify that the differential equation $\frac{dy}{dx}=\frac{x^2+xy+y^2}{x^2}$ 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

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$\frac{dy}{dx}=\frac{x^2+xy+y^2}{x^2}$

Learn how to solve differential equations problems step by step online. Solve the differential equation dy/dx=(x^2+xyy^2)/(x^2). We can identify that the differential equation \frac{dy}{dx}=\frac{x^2+xy+y^2}{x^2} 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. Group the terms of the differential equation. Move the terms of the u variable to the left side, and the terms of the x variable to the right side of the equality.

** Final answer to the problem

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