Category: 1. Differential Equations

Ordinary differential equations applications in real life are used to calculate the movement or flow of electricity, motion of an object to and fro like a pendulum, to explain thermodynamics concepts. Also, in medical terms, they are used to check the growth of diseases in graphical representation. Differential equations are useful in describing mathematical models…

The differential equation has infinitely many solutions. Solving a differential equation is referred to as integrating a differential equation since the process of finding the solution to a differential equation involves integration. A solution of a differential equation is an expression for the dependent variable in terms of the independent variable which satisfies the differential…

The differential equations are modeled from real-life scenarios. Newton’s second law is described by the differential equation where m is the mass of the object, h is the height above the ground level. This is the second-order differential equation of the unknown height as a function of time. As time increases, the population increases. If…

An equation involving only partial derivatives of one or more functions of two or more independent variables is called a partial differential equation also known as PDE. A few examples are: ?u/ dx + ?/dy = 0, ?2u/?x2 + ?2u/?x2 = 0

The differential equations are classified as: Ordinary Differential Equations Partial Differential Equations Ordinary Differential Equation The “Ordinary Differential Equation” also known as ODE is an equation that contains only one independent variable and one or more of its derivatives with respect to the variable. Thus, the ordinary differential equation is represented as the relation having…

If a differential equation is expressible in a polynomial form, then the integral power of the highest order derivative that appears is called the degree of the differential equation. The degree of the differential equation is the power of the highest ordered derivative present in the equation. To find the degree of the differential equation,…

The equation which includes second-order derivative is the second-order differential equation. It is represented as; d/dx(dy/dx) = d2y/dx2 = f”(x) = y”.

You can see in the first example, it is the first-order differential equation that has a degree equal to 1. All the linear equations in the form of derivatives are in the first order. It has only the first derivative such as dy/dx, where x and y are the two variables and is represented as:…

The order of a differential equation is the highest order of the derivative appearing in the equation. Consider the following differential equations, dy/dx = ex, (d4y/dx4) + y = 0, (d3y/dx3) + x2(d2y/dx2) = 0 In above differential equation examples, the highest derivative are of first, fourth and third order respectively.

A differential equation is an equation that contains at least one derivative of an unknown function, either an ordinary derivative or a partial derivative. Suppose the rate of change of a function y with respect to x is inversely proportional to y, we express it as dy/dx = k/y. In calculus, a differential equation is an equation that…