# Chapter 1 - First-Order Differential Equations - 1.4 Separable Differential Equations - True-False Review: i

True.

#### Work Step by Step

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.

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