**Classification of Differential Equation and Examples**

1. **Ordinary differential equation** in which all derivatives are ordinary derivatives of one or more dependent variable with respect to a single independent variable.

2. **A partial differential equation** is a differential equation containing at least one partial derivative of some dependent variable.

3. **The Order of a Differential Equation** is the order of the neglect order derivative which appears in the equation.

4. **A Differential Equation** is linear in a set of one or more of its dependent variables if and only if each learn of the equation which contains a variable of the set or any of their duration is of the first degree in those variable and their derivative.

5. **A Differential Equation which is not linear in some dependent variable** is said to be nonlinear in that variables. A differential Equation which is not linear in the set of all its dependent variable is simply said to be nonlinear.

**Example 1**

The Equation is a linear differential equation of second order the presence of product xy and the term Cos X does not alter this fact that the equation is linear because by definition linearity is determined so Let y by the way the dependent variable y. and its derivatives enter into combination away themselves within each term of the equation.

**Example 2**

The Equation is a nonlinear equation becomes of the occurrence of the product of y and one of derivatives.

**Example 3**

The Equation is linear in the dependent variable V but nonlinear in the dependent variable a because Sin U is a nonlinear function of U. The equation is also nonlinear

**Example 4**

The Equation is linear in each dependent variable x and y. However because of the term xy is not linear in the set of dependent variable (x, y) or consequence the equation is also nonlinear.

**Example 5**

The equation 3x^2 dx + (Sin x) y = 0 is neither linear or nonlinear division by dx transform it into the equation 3x^2 + (Sin x) y = 0 which is linear in y but division by dy gives 3x^2 dx/dy + Sin x = 0