This document defines and describes ordinary and partial differential equations. It states that an ordinary differential equation contains derivatives of a dependent variable with respect to only one independent variable, while a partial differential equation contains derivatives with respect to two or more independent variables. The document also defines the order of a differential equation as the highest derivative that occurs in the equation.

1. Ordinary Differential Equations
Second Order Differential Equations
by
P B L Sirisha Devi

2. Definitions
Derivative
The rate of change of a function with
respect to the variable
Differential Equation
An equation involving differentials or
one dependent variable and its derivatives with
respect to one or more independent variables
Ex: 3x+
𝑑𝑦
𝑑𝑥
+4y = 0

3. Types of Differential Equations
• Ordinary Differential Equations
• Partial Differential Equations
Ordinary Differential Equation
A differential Equation is said to be ordinary differential
equation, if the derivatives in the equation have reference only one
independent variable.
Ex: 1. 𝑥 + 2
𝑑𝑦
𝑑𝑥
+ 5 = cos 𝑥
2. 2𝑥
𝑑𝑦
𝑑𝑥
+ 4𝑦 = 6.

4. Partial Differential Equation
A differential equation is said to be partial if the derivatives in
the equation have reference of two or more independent
variables.
Ex: 2𝑥 + 1
𝜕𝑦
𝜕𝑥
+ 4
𝜕𝑦
𝜕𝑧
+ 2z = 0
Order of a Differential Equation
The order of a differential equation is highest derivative occurs in
its differential Equation.
Ex: 2𝑥
𝑑𝑦
𝑑𝑥
+ 4𝑦 = 0
Here the order is 1.