1 min readβ’june 8, 2020

Jacob Jeffries

π₯**Watch: AP Calculus AB/BC - ****Separable Differential Equations**

The separation of variables is a technique for finding **general** solutions to a differential equation. In this context, βgeneral solutionsβ means that we will be solving for a **set** or **family** of functions. This may seem like abstract wording, but this idea has already been explored in integration and antidifferentiation: π―

This statement reads as β*C* is any real number, which implies *f(x) + C* is confined to a certain set of functions *S*.β Or, more simply put, this means that there are infinite solutions to Eq. 22, but the solution must include the condition that *C* is a constant that does not depend on *x*.

This means that *f(x) + C* is a general solution. A specific solution for this same example would be: *C* is a specific number. Differential equations function in a similar way. First, find a general solution, then find a specific solution if you are given more information. π

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