1. DIFFERENTIAL EQUATIONS
TOPIC : 6.0
DIFFERENTIAL EQUATIONS

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

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

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

5. 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.

6. 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

7. 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 :

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

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

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

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

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

13. Solution

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

16. Solution
By substitution

17. Solution
Using integration by parts

19. Solution
integration of partial fractions

20. Solution