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โ™พ๏ธย ap calc

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๐Ÿ’Žย Unit 7

ย ย โ€ขย ย โฑ๏ธ1 min read

7.6 Finding General Solutions Using Separation of Variables

Jacob Jeffries

jacob jeffries

โฑ๏ธ June 8, 2020

๐Ÿ“…โŒจ๏ธ

๐ŸŽฅWatch: 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, โ€œgeneral solutionsโ€ 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: ๐Ÿ’ฏ

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This statement reads as โ€œC is any real number, which implies f(x) + C is confined to a certain set of functions S.โ€ 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. ๐Ÿ“–

To be continued in 7.7 Finding Particular Solutions Using Initial Conditions and Separation of Variables.

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