In this video, we shall learn how to solve Second order linear homogeneous differential equations.
A second order linear homogeneous diff equation is given of the form
p(x)d^2y/dx^2 + q(x)dy/dx +r(x)y = 0, where p, q and r are all functions of x.

To solve such equations with constants coefficients, we simply derive the auxiliary equation or the characteristic equation of the differential equation.
This auxiliary equation is quadratic and hence its roots can be found by the
1. method of factorization or
2. quadratic formula.

Three cases may arise
if roots are;
Case 1
real and unequal / distinct
Case 2
real and equal
Case 3
complex

00:00 - Introduction
07:50 - Nature of roots
11:13 - Real and unequal / distinct roots
13:40 - IVP: Real and unequal / distinct roots
20:45 - Real and equal / roots
22:26 - complex roots

Playlists on various Course
1. Applied Electricity
   • APPLIED ELECTRICITY  

2. Linear Algebra / Math 151
   • LINEAR ALGEBRA  

3. Basic Mechanics
   • BASIC MECHANICS / STATICS  

4. Calculus with Analysis / Calculus 1 / Math 152
   • CALCULUS WITH ANALYSIS / CALCULUS 1 /...  

5. Differential Equations / Math 251
   • DIFFERENTIAL EQUATIONS  

6. Electric Circuit Theory / Circuit Design
   • ELECTRIC CIRCUIT THEORY / CIRCUIT DESIGN  

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