Ordinary Differential Equations/Exact 2

First Order Differential Equations

This page details a method for finding the solutions to equations of the form

Using the Integrating Factor:

Example 1Edit

Consider the following equation:


Now the   So the integrating factor is:


Multiply the original equation by  


Then try:  

Which is equal to the LHS giving us:


Then integrate with respect to x:



  (This is the general solution)