Ordinary Differential Equations/Exact 2

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First Order Differential Equations

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

Using the Integrating Factor:

Example 1[edit]

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)