Separation of variables

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


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


To solve

We can rearrange the equation into


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 .


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