differential equations intro

Differential EquationsIntroduction, types, order, degree, etc

Definition, Notations

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

Partial DE

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

LDE and NLDE

• Linear Differential Equation

Exercises

Exercises

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.

Order and Degree

Solution to DE

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

Solution to DE

Initial Value Problem

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

General Solution & Particular Solution

• General Solution – solution to a DE without specific initial conditions.

• Particular Solution – solution to a DE with initial conditions

Exercises