Introduction to Differential Equations

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