## Differential Equations and Linear Algebra (4th Edition)

Factor out the expression on the right to get $$\frac{dy}{dx}=\frac{xy(x^2+xy)}{x^2+xy}=xy$$ $$\frac{dy}{dx}=xy$$ Multiplying the equation by $\frac{dx}{y}$ yields $$\frac{dy}{y}=xdx$$ Therefore, the variables can be separated and the equation must be separable.