# Section 1: Integrating Factor

### Instructions

- First, you should watch the concepts videos below explaining the topics in the section.
- Second, you should attempt to solve the exercises and then watch the videos explaining the exercises.
- Last, you should attempt to answer the self-assessment questions to determine how well you learned the material.
- When you have finished the material below, you can start on the next section or return to the main differential equations page.

### Concepts

- Definitions and terminology for ordinary differential equations
- Using an integrating factor to solve a first-order linear differential equation

### Exercises

**Directions:**You should attempt to solve the problems first and then watch the video to see the solution.

1. Solve the differential equation \(y'-2ty=t.\)

### Self-Assessment Questions

**Directions:**The following questions are an assessment of your understanding of the material above. If you are not sure of the answers, you may need to rewatch the videos.

- Can you define an ODE?
- Give an example of a \(3^{\mbox{rd}}\) order ODE, with \(t\) as your independent variable and \(x=x(t)\) as the dependent variable. Is your example an autonomous ODE?
- What is the significance of an integrating factor? How does it lead to finding the solutions of a linear, \(1^{\mbox{st}}\) order, ODE?
- Can we solve the ODE \(y'=ty+1\) using the integrating factor method? What about the ODE \(y'=ty^2+1\)? Why?