Distinct Real Roots
41 min 5 Examples
- Distinct Real Roots in Second-Order Differential Equations: Overview
- Verify the Principle of Superposition (Example)
- Determine General Form for Second-Order DEs (Example #1)
- Address Initial Conditions in Second-Order DEs (Examples #2-3)
- Find General Form for Additional Second-Order DEs (Examples #4-5)
Complex Roots
46 min 5 Examples
- Complex Roots in Second-Order Differential Equations: Overview
- Find the General Form of Second-Order DE (Examples #1-2)
- Transient Terms and Steady-State Terms: Introduction
- Solve Second-Order DE with Initial Conditions (Examples #3-4)
- Non-Constant Coefficients & Reduction of Order Introduction (Example #5)
Repeated Roots
1 hr 9 min 6 Examples
- Second-Order DEs with Repeated Roots & Reduction of Order: Overview
- Find the General Solution to the Second-Order DE (Example #1)
- Solve Second-Order DE with Initial Conditions (Examples #2-3)
- Use Reduction of Order to Find Second Independent Solution (Examples #4-6)
- Recap: Solving Second-Order Homogeneous DEs & Reduction of Order
Wronskian
45 min 6 Examples
- Differential Operators & Principle of Superposition: Overview
- Wronskian, Theorems & Facts: Overview
- Calculate Wronskian & Determine Linear Independence for 2nd-Order DE (Examples #1-4)
- Calculate Wronskian & Determine Linear Independence for 3rd-Order DE (Example #5)
- Abel’s Theorem: Overview & Example
- Wronskian Calculation Using Abel’s Theorem (Example)
Undetermined Coefficients
1 hr 16 min 14 Examples
- Overview of Undetermined Coefficients – Superposition Approach
- More on Undetermined Coefficients: Hints and Warnings
- Write the Form of the Particular Solution (Examples #1-9)
- Find the General Solution to Inhomogeneous DE (Examples #10-14)
Differential Operators
1 hr 48 min 9 Examples
- Quick Review: Differential Operators with Examples
- Apply the Differential Operator to Functions (Examples #1-2)
- Annihilator Method Overview
- Find a Differential Operator that Annihilates Functions (Examples #3-6)
- Use the Annihilation Method to Find the General Solution (Example #7)
- Solving Systems by Elimination Overview
- Solve Systems by Elimination (Examples #8-9)
Variation of Parameters
1 hr 9 min 5 Examples
- Overview of Variation of Parameters Method
- Find the General Solution to Inhomogeneous DEs with Non-Constant Coefficients (Examples #1-2)
- Find the General Solution to Inhomogeneous DEs (Examples #3-5)
Cauchy Euler Equation
23 min 6 Examples
- Overview of the Cauchy-Euler Equation
- Find the General Solution Using the Cauchy-Euler Equation (Examples #1-6)
Mechanical Vibrations
1 hr 15 min 6 Examples
- Overview of Mechanical Vibrations
- Free-Undamped Vibrations: Steps & Displacement (Example #1)
- Free-Damped Vibrations: Steps & Displacement
- Critical Damping (Example #2)
- Over Damping (Example #3)
- Under Damping (Example #4)
- Forced Vibrations: Steps & General Solution
- Forced-Undamped System without Resonance (Example #5)
- Forced-Damped System with Resonance (Example #6)
Chapter Test
1 hr 47 min 8 Practice Problems
- Determine Linear Independence Using Wronskian (Problem #1a-c)
- Homogeneous DE: Distinct Real Roots (Problem #2a)
- Homogeneous DE: Distinct & Repeated Roots (Problem #2b)
- Homogeneous DE: Repeated & Complex Roots (Problem #2c)
- General Solution: Undetermined Coefficients Method (Problem #3)
- Particular Solution: Variation of Parameters (Problem #4)
- General Solution: Reduction of Order Method (Problem #5)
- System Solution: Differential Operators (Problem #6)
- Non-Homogeneous Cauchy-Euler Equation (Problem #7)
- Damping Constants for Over, Critically, and Underdamped Motion (Problem #8a-c)