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Outline for Lecture 2
1
st
order Differential Equations
2. Sources of Differential Equations (DE):
2.1 Mathematical Manipulations
e.g. 1.
If A and B are constants and
We can see
Thus,
Therefore, we can say DE
has a solution
e.g.2. General DE
The most general form of nth order DE with independent variable x and unknown
function y(x) and dependent variable x
where F is specific realvalued function with (n+2) variables: x, y, y’, y’’, …
Solution to a DE:
A function u(x) is a solution of the above DE on interval “I” provided
that all derivatives,
exist on “I” and
for all x in “I”.
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View Full Documente.g.3. Ordinary DE and Partial DE
Ordinary DE
’s unknown function has ONLY ONE independent variable.
In the above equation, “y” is the unknown function with one independent variable “x”.
Partial DE
’s unknown function has two or more independent variables.
In the above equation, “y” is the unknown function with two independent variables x1
and x2.
2.2 Practical Applications
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 Summer '08
 Staff

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