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)