23/10/2025
334/1000 | "Solving Non-Homogeneous Linear Differential Equations with Constant Coefficients"
Playlist of Non-Homogeneous Differential Equations - https://youtube.com/playlist?list=PLT2xRiy9TL2jK-xYUnfnQG3balCBGFmD4&si=UeXiYmiA_VoJpjbh
In this Video, we will learn:
00:00 Non-Homogeneous Linear Differential Equation with Constant Coefficients
02:25 Solution of NON-HOMOGENEOUS LINEAR DIFFERENTIAL Equation
02:40 How to Find Complementary function
03:00 How to convert Differential Equation in Auxiliary or Characteristics Equation
05:30 Roots of Auxiliary Equation when real and distinct roots
06:00 Solution of Complementary function when real and distinct roots
06:50 General formula to Find Particular Integral
07:10 How to Find Particular Integral when R(x) = e^(ax)
08:20 Formula of Operator Method when R(x) = e^(ax)
10:15 How to Find Particular Integral when R(x) = sin(ax+b) or cos(ax+b)
14:40 Complete Solution of Non-homogeneous Differential Equations
# Description
"Learn how to solve non-homogeneous linear differential equations with constant coefficients. In this video, we'll cover:
- Introduction to non-homogeneous linear differential equations
- Finding the complementary function
- Converting differential equations to auxiliary equations
- Solving auxiliary equations with real and distinct roots
- Finding particular integrals using operator methods
- Particular integrals for R(x) = e^(ax), sin(ax+b), and cos(ax+b)
- Complete solution of non-homogeneous differential equations
Whether you're a student of differential equations, engineering mathematics, or physics, this video is for you. We'll break down complex concepts into easy-to-understand language and provide step-by-step examples.
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# Hashtags
# Keywords
non-homogeneous differential equations, constant coefficients, complementary function, particular integral, operator method, dif
