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To solve the differential equation \( (2x + 3y) \, dx + (3x + 4y) \, dy = 0 \), you can first rearrange it into the standard form. This can also be viewed as a relationship between two variables that maintains conservation. Look for potential functions or separable methods to find solutions that represent curves in the xy-plane. In real-world applications, such differential equations can model various phenomena, such as mixing ratios in chemical processes or even population dynamics. By solving them, we can uncover equilibrium states or trajectories that might describe how species or substances interact over time, helping, for example, in resource management or ecological balance.
