**Separation of variables** is a technique of solving a specific type of differential equations.

## Definition

An ordainary differential equation is called **separable** if the following criteria can be satisfied through rearranging the equation:

## Example

To solve

We can rearrange the equation into

Integrating:

Which gives

Since and are arbitaray constants, we can group them together and give

The answer is usually leave at the form described above instead of isolating .

## References

- D. Lomen and D. Lovelock,
*Differential Equations Graphics. Model. Data.*, John Wiley and Sons, Toronto, 1999. - Separation of variables on Wolfram Mathworld