Homogeneous Second-Order Linear Differential Equations

This course develops methods for solving homogeneous second-order linear differential equations, including characteristic equations with distinct or repeated roots and reduction of order. It also examines linear dependence and independence of functions and extends the characteristic-equation method to higher-order equations.

Syllabus

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.