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Μάθημα: AP®︎ Λογισμός BC > Ενότητα 7
Μάθημα 6: Finding general solutions using separation of variables- Separable equations introduction
- Addressing treating differentials algebraically
- Separable differential equations
- Separable differential equations: find the error
- Worked example: separable differential equations
- Separable differential equations
- Worked example: identifying separable equations
- Identifying separable equations
- Identify separable equations
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Identifying separable equations
To solve a differential equation using separation of variables, we must be able to bring it to the form where is an expression that doesn't contain and is an expression that doesn't contain .
Not all differential equations are like that. For example, cannot be brought to the form no matter how much we try.
In fact, a major challenge with using separation of variables is to identify where this method is applicable. Differential equations that can be solved using separation of variables are called separable equations.
So how can we tell whether an equation is separable? The most common type are equations where is equal to a product or a quotient of and .
For example, can turn into when multiplied by and .
Also, can turn into when divided by and multiplied by .
Here are a few concrete examples:
Other equations must be slightly manipulated before they are in the form . For example, we need to factor the right-hand side of to bring it to the desired form:
Want more practice? Try this exercise.
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