Nonhomogeneous Equations
Reference: Logan, A First Course in Differential Equations, 3rd ed., §2.3 "Nonhomogeneous Equations", pp. 100-115
Textbook Reference
| Primary source | Logan, A First Course in Differential Equations, 3rd ed., §2.3 “Nonhomogeneous Equations”, pp. 100-115 |
| Read this week | Week 5 of the quarter: pages 100 to 115 |
Bring your copy of Logan to this topic. The section and pages above are the exact reading for this skill.
Objectives
By the end of this section you should be able to:
- Write the general solution as the homogeneous solution plus a particular solution
- Use undetermined coefficients for constant, polynomial, exponential, and sinusoidal forcing
- Recognize resonance, when the forcing matches the homogeneous response, and multiply the guess by t
- Split a sum of forcing terms with superposition and add the particular solutions
Prerequisite Check
Before this section, make sure you are comfortable with:
- Solving the homogeneous constant-coefficient equation
- Differentiating exponentials, sines, cosines, and polynomials
Status
This is a guided stub. It gives you the exact Logan reading with page numbers, the week it lands in the quarter, the learning targets, and what to review first. The full worked examples and the leveled practice set for this section are being written and will appear here.