Separation of variables

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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 .


Reference

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