Let us recall the definition of** *** ‘derivative’.* A derivative, particularly in mathematics is the

*rate of change of function with respect to a variable*. For example, in , you will notice the rate of change of w.r.t variable which shows the slope of curve or we can call it as .

We denote derivative by i.e., the change in with respect to . If is a function, the derivative is represented as . Therefore, we can say that .

*“In mathematics, a **differential equation(DE)** is an equation that relates one or more functions and their derivatives.In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two.”*

Let’s split the terms of Differential Equation.

By now, we are aware that ‘Differentiate‘ means “*Computing a derivative*“, similarly ‘Differential Equation’ means “*Equation containing a derivative*“.

Few examples of DE:

__NOTE: __

- For standard equations, the solution is a scalar value. (Example: which results to )
- For Differential Equations, the solution is a function. (Example: which results to )

The** ORDER** of a differential equation is the *order of the highest derivative* or differential coefficient present in the equation.

Let us understand this by few examples:

*classify*DE on the basis of its Order as

**FIRST ORDER DIFFERENTIAL EQUATION**and

**SECOND ORDER DIFFERENTIAL EQUATION**.

The **DEGREE **of the differential equation is the * power of highest order derivative *in the equation.

There are three basic types of differential equations.

- Ordinary (ODEs)
- Partial (PDEs)
- Differential-algebraic (DAEs)