SECOND-ORDER LINEAR ODEs
SECOND-ORDER LINEAR ODEs
"Mathematics is the most beautiful and most powerful creation of the human spirit".
- Stefan Banach
Introduction:
We have studied about the basic concepts about ordinary differential equations in our 12 th std. In chap 10 (vol 2) we have studied about first order differential equations and how to solve them . Solving a differential equation is nothing but to integrate the equation. In this chapter we are going to concern on the second order linear ODEs and how to solve them by using some methods.
Applications:
Many important applications in mechanical and electrical engineering are modeled by linear ordinary differential equations of the second order. Their theory is representative of all the linear ODEs as is seen when compared to linear ODEs of third and higher order, respectively.
Types of ODEs
1. Homogeneous ODEs
a. Homogeneous Linear
b. Homogeneous non linear
2. Non Homogeneous ODEs
a. Non Homogeneous linear
b. Non Homogeneous non linear
The detailed definition of homogeneous ODEs are explained in the below PDFs.
Homogeneous Linear ODEs of second order: Exercise 2.1: https://drive.google.com/file/d/1YkG20ro_2YuWzvuYlzbF-bieW5nHPpwI/view?usp=drivesdk
Homogeneous Linear ODEs with constant coefficients: Exercise 2.2: https://drive.google.com/file/d/1Ym2t9ZK-TPUKI5iIXYr_NSmF7sM9QGEp/view?usp=drivesdk
Euler - Cauchy Equations: Exercise 2.5:
Existence and uniqueness of solutions . WRONSKIAN CONCEPT
Exercise 2.6:
Non Homogeneous linear ODEs
Exercise 2.7:
MODELING: ELECTRIC CIRCUITS
Exercise 2.9:
SOLUTION BY VARIATION OF PARAMETERS
Exercise 2.10:
