🔵18 - Second Order Linear Homogeneous Differential Equations with Constants coefficients
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In this video, we shall
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
Make sure to watch till the end.
Like, share, and subscribe.
Thank you.
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
Make sure to watch till the end.
Like, share, and subscribe.
Thank you.
- #education
- #second_order_linear_homogeneous_differential_equations
- #skancity_second_order_linear_homogeneous_differential_equations_more_solved_examples
- #second_order_linear_homogeneous_differential_equations_more_solved_examples
- #2nd_order_linear_homogeneous_diff_equations
- #homogenous_2nd_order_linear_diff_equations
- #2nd_order_homogeneous_differential_equations
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