1. **Stating the problem:** We are given the differential equation $$y' = \frac{x^2 + xy}{xy}$$ and asked to write it in homogeneous form. 2. **Recall the definition:** A differential equation is homogeneous if it can be expressed as $$y' = f\left(\frac{y}{x}\right)$$ or equivalently if the right side is a function of the ratio $\frac{y}{x}$ only. 3. **Simplify the given equation:** $$y' = \frac{x^2 + xy}{xy} = \frac{x^2}{xy} + \frac{xy}{xy} = \frac{x}{y} + 1$$ 4. **Rewrite in terms of $v = \frac{y}{x}$:** Since $v = \frac{y}{x}$, then $\frac{x}{y} = \frac{1}{v}$. 5. **Substitute back:** $$y' = 1 + \frac{1}{v}$$ 6. **Conclusion:** The equation is homogeneous because the right side depends only on $v = \frac{y}{x}$. **Final homogeneous form:** $$y' = 1 + \frac{1}{\frac{y}{x}} = 1 + \frac{x}{y}$$