Linear Differential Equations

where and are functions of (or constants).

Method: Integrating Factor

The solution is:

Steps to Solve

1. Write in standard form:
2. Find the integrating factor:
3. Multiply both sides by IF
4. Integrate both sides
5. Solve for

Example: Basic Linear Equation

Solve .

Example: Linear Equation with Initial Condition

Solve with .

Bernoulli's Equation

Example: Bernoulli Equation

Solve .