In Maths, the differential equation is defined as an equation that relates one or more than one functions and their derivatives. Here, the function defines the physical quantities, and derivatives define the rate of change of the given function. The differential equation can be classified into many types based on the equation. The equation can be linear or nonlinear, ordinary or partial, or homogeneous or heterogeneous. The different types of differential equations are encountered in many disciplines like Physics, Biology, Economics, and Engineering. For example, partial differential equations are used to describe various phenomena such as heat, sound, elasticity, and so on. It also helps to explain the exponential growth or decay, the population growth of the species. Here, let’s discuss some of the essential applications of differential equations in various fields.
Physics
In physics, the differential equations play a prominent role in understanding the most important phenomena in nature. It provides a great insight to understand the process using the differential equations. For example, the interaction between atoms and molecules, fluid flow, and material change using the chemical process at the microscopic level are understood easily with differential equations. Most of the ordinary differential equations encountered in Physics are linear.
Biology
Cell biology is one of the most active and fast-growing interdisciplinary areas, which involves many mathematical concepts and techniques. In developmental medicine and bioengineering, many models and methods are applied to various problems that use different approaches. One of the important processes used in molecular biology is differential equations, which leads to significant advancement in bioengineering. For example, ODEs are used in various biological areas ranging from DNA molecules or the biosynthesis of phospholipids on the cellular level.
Economics
In economics, the differential equation is considered an essential tool in economic analysis. The modern theory of differential equations helps to comprehend the contemporary literature of economics. The differential equations are used to model the behaviour of many complex processes. For instance, the change in the GDP of the economy over time can be calculated with differential equations. It can be calculated by taking the rate of change of Gross Domestic Product (GDP) proportional to the current GDP.
Engineering
In engineering, differential equations have numerous applications, and engineers should be able to model the physical problems using mathematical equations. Many engineering principles and scientific laws are generally described using differential equations. Most of the special functions are characterized as the solutions of the linear differential equations. Engineers always use differential equations to understand the system’s behaviour by creating the mathematical model such as electrical circuits, hydraulic flow, heat transfer, and so on.
Apart from the applications, the differential equations are used to create software, bots, artificial intelligence, computer games, etc. Thus, the differential equation is an essential tool to describe the nature of the physical universe, and almost all the laws of physics and chemistry use the differential equation.
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