# Differential Equations

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) d2y/dx2 = x ln(dy/dx)

Solution:
(i) The given differential equation can be re-written as y = edy/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)

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