This concept covers solving separable first-order differential equations, in which the equation can be algebraically rearranged so that all terms involving the dependent variable (with its differential) appear on one side and all terms involving the independent variable (with its differential) appear on the other, allowing both sides to be integrated independently. The method, known as separation of variables, produces an implicit (or, after solving for the dependent variable, explicit) general solution containing an arbitrary constant of integration, which can only be determined given an initial condition. This situates the topic within the theory of ordinary differential equations as an application of antidifferentiation and inverse trigonometric/algebraic manipulation.
This concept covers solving separable first-order differential equations, in which the equation can be algebraically rearranged so that all terms involving the dependent variable (with its differenti…