Variable Coefficients and Reduction of Order
Reference: Logan, A First Course in Differential Equations, 3rd ed., §2.4 "Variable Coefficients and Reduction of Order", pp. 116-126
Textbook Reference
| Primary source | Logan, A First Course in Differential Equations, 3rd ed., §2.4 “Variable Coefficients and Reduction of Order”, pp. 116-126 |
| Read this week | Week 6 of the quarter: pages 116 to 126 |
Logan §2.4, pages 116 to 126, is the reading for the Cauchy-Euler equation and reduction of order.
Objectives
By the end of this section you should be able to:
- Solve a Cauchy-Euler equation by assuming t to the m and solving the indicial equation
- Handle the distinct-real, repeated, and complex cases of the indicial equation
- Use reduction of order to find a second solution when one solution is known
- Avoid the domain pitfall at t equals zero in a Cauchy-Euler equation
Prerequisite Check
Before this section, make sure you are comfortable with:
- Constant-coefficient equations and superposition
- Properties of logarithms
- Integration by parts
Status
Worked examples and a leveled practice set for the Cauchy-Euler equation and reduction of order are still in progress.