1. Sec 5.5:Variation of Parameters
Consider the following non-homog DE:
be two linearly indep solution for the associated homog.
then a particular solution for (*) is

2. Sec 1.1: Differential Equations and Mathematical Models
Definition: Differential Equation 1
An equation containing the derivatives of one or more dependent variables with respect to one or more independent variables, is said to be a differential equation (DE) 2

3. Sec 1.1: Differential Equations and Mathematical Models2 6 3 4 7 5

4. Classification 8 9 Classification By Type Order
Sec 1.1: Definitions and Terminology
Classification 8 9
Classification By
Order
Type

5. Classification By Type
Classification By Type (ODE,PDE)
Classification By Type
If an equation containing only ordinary derivatives  it is said to be Ordinary Differential Equation (ODE)
An equation involving partial derivatives  it is said to be Partial Differential Equation (PDE) 8 1

6. Classification By Order
The order of a differential equation (ODE or PDE) is the order of the highest derivative highest derivative in the equation.
Classification By Order 3 1 4 2 5
. n-th order DE

7. Classification Classification By Type Order ODE or PDE
highest derivative
Type
Order

8. System of DE System of two Ordinary Differential Equations
2ed order, linear, ODE

9. Navier-Stokes Equations
ODE or PDE
order??
One Million Dollar

10. Sec 1.1: Differential Equations and Mathematical Models
Definition: Solution of an ODE
A continuous function is said to be a solution of a DE if it satisfies the DE on an interval I

11. Sec 1.1: Definitions and Terminology
Families of Solutions
What diff?????

12. Sec 1.1: Definitions and Terminology
Families of Solutions
One-parameter family of solutions
Two-parameter family of solutions
n-parameter family of solutions
Particular Solution: A solution of DE that is free of arbitrary parameters

13. Sec 1.1: Definitions and Terminology
Trivial Solution
y=0 is said to be trivial solution
Singular Solution
sometimes a DE has a solution that is not a member of a family of solutions. This solution is called singular solution
one-parameter family of solutions
Verify??
Not a member of the family no value for c

14. Office Hours

15. Piecewise-Defined Solution Explicit and Impicit Solutions
Sec 1.1: Definitions and Terminology
Piecewise-Defined Solution
Verify??
Explicit and Impicit Solutions
Explicit Solution
Verify??
Implicit Solution

16. Sec 1.1: Homework Problems

17. Sec 1.1: Homework Problems