Integrating Factor Method

1. Put your equation into the above form.
2. Extract and place into the equation to get our integrating factor.
3. Multiply both sides by .
4. Reverse the product rule on the left side.
5. Integrate both sides.
6. Solve for the constant of integration and put into explicit form.

See W1L9 - Intro to Linear Differential Equations and Integrating Factors and W1L10 - Solving Linear Differential Equations with an Integrating Factor for examples.

Starting with an equation in the form:

Essentially you are undoing a product rule. The product rule that occurred is as follows:

One should see that the right side of the above equation is very similar to the left side of our original equation, only that there is an extra in front.

In short terms we cannot simply just integrate to find . Instead we need to find :

From here we can multiply both sides by to put the equation in a format that matches the output of the product rule and then undo the product rule. See W1L9 - Intro to Linear Differential Equations and Integrating Factors for more details.

• W1L9 - Intro to Linear Differential Equations and Integrating Factors
• W1L10 - Solving Linear Differential Equations with an Integrating Factor