This document introduces differential equations, including definitions of ordinary and partial differential equations. Ordinary differential equations relate a function to one independent variable and its derivatives, while partial differential equations relate a function of two or more variables to its partial derivatives. The document discusses the order and degree of differential equations, and explains that the order is the highest derivative and the degree is the highest order of the derivative. It also defines the solution to a differential equation, initial value problems, and the difference between general and particular solutions.

1. Differential
Equations
Introduction, types, order, degree, etc

2. Definition, Notations

3. Ordinary DE
• Ordinary Differential Equation is one which relates a
function y = f (x) to one independent variable x and its
derivative/s. Assuming that y is a function of x, the
following are examples of ODE

4. Partial DE
• A partial differential equation is one which relates a
function of two or more variables to its partial
derivatives.

5. LDE and NLDE
• Linear Differential Equation

6. Exercises

7. Exercises

8. Order and Degree
• Order of DE – the highest order of derivative contained in
the equation.
• Degree of DE – the degree of the highest order of
derivative contained in the equation.

9. Order and Degree

10. Solution to DE
• Solution to DE – is a function y = f(x) that satisfies the
differential equation.

11. Solution to DE

12. Initial Value Problem
• Initial Value Problem – a differential equation which
supplies a numerical value for some of its derivative at
some point (x, y)

13. General Solution &
Particular Solution
• General Solution – solution to a DE without specific
initial conditions.
• Particular Solution – solution to a DE with initial
conditions

14. Exercises