Higher Order Linear Differential Equations

[Virtual Presenter] Good morning everyone! Today I am going to talk to you about higher order Linear Differential Equations; what they are how they can be applied and the examples of how they are used in everyday scenarios. I am sure you will find this topic interesting! Let's get started!.

[Audio] A differential equation is a mathematical equation that relates some function with its derivatives. Higher order differential equations involve derivatives of order two or greater. To begin with let's look at the definition and applications before concluding..

[Audio] Differential equations are equations that relate an unknown function to its derivatives. The order of a differential equation is determined by the highest derivative present in the equation and the coefficients refer to the constants that multiply the derivatives. A solution to a differential equation is a function that satisfies the equation when substituted into it. Higher Order Linear Differential Equations are differential equations of order greater than one with linear coefficients. Now we have the basics of Higher Order Linear Differential Equations..

[Audio] An equation of the first order linear differential type is an equation that can be written as (dy/dx) plus P(x)y = Q(x). This equation has numerous applications in various fields such as population growth cooling of objects economics and physics. For example it can be used to describe the rate of population growth over time; the rate at which an object cools down; economic growth and decay; and the rate of change of physical quantities in different systems..

[Audio] A Higher Order Linear Differential Equation involves derivatives of a function up to the nth order. It has two variables the dependent variable y and the independent variable x along with a forcing function f(x). We will go through the fundamentals of these equations in detail..

[Audio] We will now look at some of the applications of higher order linear differential equations in physics. These equations are used for modelling oscillations from a mass-spring system to the behavior of a pendulum. They are also handy for studying wave propagation such as sound waves and electromagnetic waves in different mediums..

[Audio] This slide examines the utilization of higher order linear differential equations. The table displays the equation its explanation and its utilization in population growth investment and depreciation as well as economic oscillations. This is an effective instrument used to create models of various economic and population movements as well as their respective speeds of alteration. By solving these equations we can gain significant insights into the behavior of distinct economic and population frameworks and make informed choices regarding the best techniques to use..

[Audio] Higher order linear differential equations with constant coefficients are used across many fields for understanding and modeling complex real world systems. From oscillating systems and electrical circuits to population growth and economic fluctuations these equations are useful in physics and engineering economics biology and computer science. They can also be applied in various computer science applications such as image and signal processing and machine learning algorithms allowing us to unlock the potential of these equations..

THANK YOU.