Chapter 1 - First-Order Differential Equations - 1.4 Separable Differential Equations - True-False Review - Page 43: f

True.

Work Step by Step

Using exponent rules, $e^{x+y}$ can be changed to $e^xe^y$. This changes the equation to $$\frac{dy}{dx}=e^xe^y$$ The variables can be separated by multiplying the entire equation by $\frac{dx}{e^y}$. $$\frac{dy}{e^y}=e^xdx$$ Therefore, the equation is separable.

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