Ordinary Differential Equations/Exact 2

< Ordinary Differential Equations

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:

 

Giving:

 
  (This is the general solution)