There can be an obvious doubt regarding why we need to learn and understand differential equations! Are we making use of it in our lives once after? All these may be answered through simple solutions as they find applications in a variety of fields. Leaving the physics apart, and if you are into the biological arena, then it is not going to grip off of you. In biology and economics, differential equations help in modelling the behaviour of complex systems in different ways. Differential equations play a crucial role in the mathematical modelling of physical systems; certain fundamental laws of physics and chemistry are formulated as differential equations. Engineers need to make the most out of it, as they cannot remove it from their career prospects. So if it seems to interest you, then there are a few of the selected courses on the subject to look up to.

**1. Introduction to Ordinary Differential Equations by Kaist at Coursera**

The course covers the basics of the major terms that are to be understood regarding the theory of differential equations proceeding to the methods to come up with the solutions of various types of ordinary differential equations. First-order differential equations followed by the second-order linear differential equations are considered in detail. Certain solid mathematical modelling problems are also included in the course and are made to be solved using the methods introduced in this course. The classes are well detailed and are provided with the required reference material if needed. Video lectures are provided for teaching, and the completion of each module is ensured with quizzes to make sure of the topics previously taught.

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**2. Interpret and Solve Differential Equations by edx**

The main focus of the course is to make the learner able to use the differential equations to model real-world phenomena, solving the linear differential equations, proper using of matrix methods to solve the differential equations; use graphical methods to know about the behaviour of linear and non-linear systems; formulation and solving of eigenvalue and eigenvector problems; finding solutions for ODEs and separable PDEs using Fourier series inputs and boundary conditions. Differential equations are the language of the models used to explain the surroundings. The course takes the learner along with to discover the temperature, spring systems, circuits, population growth, biological cell motion, and several other illustrations to show the use of differential equations model nearly the whole lot. Certain mathematical tools are developed which helps to solve linear differential equations and understand 2×2 systems of first-order linear and nonlinear differential equations. The providers also introduce the use of linear algebra to solve systems of more than two differential equations. The use of the Fourier series is also done to analyze the behaviour and solving of ordinary differential equations (ODEs) and separable partial differential equations (PDEs). The last course considers frequency domain and Laplace transformation to understand their effects on mechanical and electrical systems.

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**3. Differential Equations in Depth by Udemy**

The course has it all about Differential Equations. They are a class of equations that occupies the use of differentials (derivatives) in their construction. They find uses in science, predominantly in physics, for modelling the actual world phenomena such as the propagation of waves. The course takes care of the ordinary differential equations (ODEs) both first and second-order; Laplace Transform and Fourier Series; Partial differential equations (PDEs) such as the common equations such as the Wave Equation and the Heat Conduction Equation; numeric solutions of differential equations including Euler’s Method, Runge-Kutta; and the Modeling and solving of the differential equations using MATLAB and Maple. The course takes an in-depth course helping in solving different types of differential equations, exploring the tricks and shortcuts to reach the solutions faster, solving equations numerically as well as analytically, and learning to use** **MATLAB to solve differential equations.

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**4. Differential Equations by MIT OpenCourseWare**

They are the language in which the laws of nature find their expression. Understanding the properties of the solutions of these equations seems to be the basis when most of the current science and engineering are concerned. Ordinary differential equations (ODE’s) agree with the functions of a single variable. The uses vary accordingly in assorted sectors. In order to check the growth of diseases using a graphical representation, the differential equation knowledge comes to play. There are several the areas like chemistry, economics and much more that makes use of the concept. If the movement or flow of electricity need to be monitored, or the movement of an object back and forth, or if the concepts of thermodynamics need to be explained, everything has to take the help of differential equations.

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**5. Elementary Differential Equations Online College Course by University of North Dakota**

As the name denotes, the elementary course takes care of the elementary techniques put to use to find the solutions using differential equations. The major topics included in this mathematics online elementary course are the Laplace transforms, Introduction to matrix theory and the Systems of differential equations. It makes use of the elementary differential equations by elementary techniques.

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**6. Differential Equations for Engineers** **by Class Central**

The course is specifically for engineers and is mediated by The Hong Kong University of Science and Technology. It is about the differential equations and incorporates the materials inevitable for the engineers. The theoretical and the application basics are included in the program. The starting of the course takes off with the understanding of the ordinary differential equations, followed by the partial differential equations. The course comes along in the form of short video lessons accompanied by simple problems to find the solution after each class. 56 such classes are shared. Quizzes follow for practice. A total of 6 weeks is assigned for the complete accomplishment of the course. The progress can be monitored by the learner itself through such practice activities.

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**7. Differential Equations Online Course** **by Distance Calculus at Roger Williams University**

Differential Equations are best known as Higher-Level Integration Theory. The simpler ones have solutions that are simple Integrals. But the complexity increases rapidly with the upheaval leading to even more complex solutions. The issues arising from the physics situations are understood to be solved through the understanding of physics as per the physicists, but regrettably, most of them are difficult to be solved algebraically. The prescribed online course on differential equations deals with it in a slightly different way; it takes the learner through various ways of reaching the concepts of Differential Equations from a laboratory-science approach. The course is considered as a study of Ordinary Differential Equations and is known in a variety of names as it includes the vivid area of application.

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**8. Differential Equations by Khan Academy**

The class provided in the context moves forward with the worked-out examples to the learners to get a complete and steady understanding of solving such equations. Certain other related areas such as Newton’s Law of Cooling and Dirac delta function, complex roots and undetermined coefficients and many others are included in the course. The first-order differential equations; their introduction, scope, areas of use, and the methods that can be adopted to solve them, the exponential models, exact equations and integrating factors, equations; The second-order linear equations, Linear homogeneous equations, Complex and repeated roots of the characteristic equation, Method of undetermined coefficients, Laplace transform, Laplace transform to solve a differential equation all are considered well in the course.

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**9. Introduction to Differential Equations at Youtube**

The course is intended particularly for engineers. It mainly involves the classification of differential equations into ODE or PDE, order, linear or nonlinear. Some examples are explained. Several of the engineering streams make use of the differential equation concept for engineering systems like hydraulic flow, heat transfer, and level controller of a tank, vibration isolation, and electrical circuits. In the case of electrical engineering, the Laplace transform methods are taken into concern for solving the differential equations. This mainly helps in reducing the differential equation problems to algebraic arrangement making it more comfortable to be solved. Differential equations have an outstanding capability to envisage the system around us. The engineers find the important aspects of modelling the issues in the area of physics, making use of the mathematical equations and then ultimately finding solutions to these problems in order to understand the performance of the systems that are involved. They find use in a vivid range of disciplines such as biology, economics, physics, chemistry and engineering. The extended applications of the varied sectors of the engineering domain find the use of differential equations.

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**10. Ordinary Differential Equations and Applications by NPTEL**

An equation for a function with one or more of its derivatives is what a differential equation is. The types of differential equations are introduced and classified. Then the learner is taken through the Euler method to solve a first-order ordinary differential equation numerically. The analytical methods for solving separable and linear first-order ODEs are also included. The explanation of the theory is followed by the wonderful illustration of the simple ODEs. The course is ultimately completed with the three real-world examples of first-order ODEs. These include; compound interest, the terminal velocity of a falling mass, and the resistor-capacitor electrical circuit.