DIFFERENTIAL EQUATIONS TOPIC : 6.0 DIFFERENTIAL EQUATIONS

LECTURE 1 of 4 6.1 Introduction Of DE 6.2 Separable Variables and Linear Equations

Objectives: a) define differential equations, b) understand degree, order and solution, c) define separable differential equations, d) solve separable differential equations.

Given y = 3x2 + x - 2 y = 3x2 + x - 2 Now reverse the process : Given Solution y = 3x2 + x - 2

A differential equation (DE) is an equation which relates an independent or dependent variable with one or more derivatives. EXAMPLES : A solution for a DE is a function that is independent from derivatives and satisfy the differential equation.

Order is the highest derivative in a differential equation. DEFINITION : Order is the highest derivative in a differential equation. Degree is the highest power of the highest derivative which occurs in a differential equation. Order = 2 EXAMPLES : Degree = 1

In this topic, we will only focus on first order and first degree DE EXAMPLE ORDER DEGREE 1 1 2 1 In this topic, we will only focus on first order and first degree DE NOTE :

Two types of solution for differential equations General solution - contains an arbitrarily constant c. Particular Solution - Given initial conditions

EXAMPLE : Given y = x2 + c. General solution If x = 1, y = 4, then y = x2 + 3. Particular solution

Differential Equations with Separable Variables A differential equation is separable if it can be written in the form of

of separable variable type Methods for solving DE of separable variable type i) Separate the variables ii) Integrate both sides

EXAMPLE 1 Find the general solutions of the following differential equations :

Solution

EXAMPLE 2 For each of the DE, find a solution that satisfies the given conditions:

Solution By substitution

Solution Using integration by parts

Solution integration of partial fractions

Solution