By a **differential equation** we mean an equation involving independent variable , dependent variable and the differential coefficients of the dependent variable i.e. it will be an equation in x, y and derivatives of y w .r .t x. e.g.

#### Order and Degree of a Differential Equation:

The order of the **highest differential coefficient** appearing in the differential equation is called the **order of the differential equation** ,

while the **exponent of the highest differential coefficient **, when the differential equation is a polynomial in all the differential coefficients, is known as the **degree of the differential equation.**

**Example 1**. Find the order and degree (if defined) of the following differential equations:

(i) y = 1 + dy/dx + (1/2!)(dy/dx)^{2} + (1/3!)(dy/dx)^{3} + ……

(ii)

(iii) d^{2}y/dx^{2} = x ln(dy/dx)

**Solution:**

(i) The given differential equation can be re-written as y = e^{dy/dx}

⇒ dy/dx = ln y . Hence its order is 1 and degree 1.

(ii) The given differential equation can be re-written as

Hence its order is 2 and degree 1.

(iii) Its order is 2. Since the given differential equation cannot be written as a polynomial in all the differential coefficients, the degree of the equation is not defined.

**Exercise 1: **

Find the order and the degree of the following differential equations

(i)

(ii)

(iii)

(iv)