Homogeneous Second-Order Linear Differential Equations

Explore homogeneous second-order linear differential equations in this comprehensive video lecture. Delve into auxiliary equations (also known as characteristic equations) with distinct and repeated roots, and learn about the reduction of orders technique. Cover topics such as second-order differential equations with constant and variable coefficients, methods for checking linear dependence and independence of functions, and solving higher-order homogeneous linear differential equations using auxiliary equations. Gain a thorough understanding of these mathematical concepts through detailed explanations and practical examples.

Second order homogeneous linear differential equations with constant coefficients.
Auxiliary equations with repeated roots.
Reduction of orders, 2nd order differential equations with variable coefficients.
Check for Linear Dependence (of 2 functions).
Check for Linear Independence (2 functions).
Check for Linear Dependence (3 functions, using definition).
Check for Linear Independence (3 functions, using definition).
Check if 3 functions are LD or LI, Q1a.
Check if 3 functions are LD or LI, Q1b.
Check if 3 functions are LD or LI, Q1c.
Higher order homogeneous linear differential equation, using auxiliary equation, sect 4.2#37.