1. Linear Equations A linear first-order DE looks like Standard form is
To solve first-order linear DEs, we will be using the term , called the integrating factor.

2. Solving first-order linear DE
Put into standard form
Find the integrating factor
Multiply both sides of the DE by the integrating factor. The result will be:
Integrate both sides of the equation.

3. Ex. Solve

4. Ex. Solve
Transient terms are terms that approach zero as x goes to infinity.

5. Ex. Solve
What is the interval of definition?

6. Ex. Solve

7. Ex. Solve

8. Ex. Solve

9. Ex. Solve , where