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Title: Differential Equations - Classifications
Description: Easy to read, clear, concise and easily understandable notes, for people who don't have the time to read through lengthy textbooks. Suitable for Year 1 University students and up, and requires little background understanding.
Description: Easy to read, clear, concise and easily understandable notes, for people who don't have the time to read through lengthy textbooks. Suitable for Year 1 University students and up, and requires little background understanding.
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Differential Equations
Definition
A differential equation: an equation containing the derivative of a dependent variable(s)
with respect to independent variable(s)
...
∂x
(II) More than one independent variable
...
Eg:
d2 y
dy 3
+ 7 ( ) - y = ex
dx
dx 2
n=2
n=1 2>1
Therefore, Order: 2
Linearity
Linear Ordinary Differential Equations must have these two properties:
(I) The power of each term containing the dependent variable is 1
...
power of one
^
^
dy
Eg: a1 (x)
+ a0 (x)y = f(x)
dx
^
^
coefficients depend on x(or constant)
Title: Differential Equations - Classifications
Description: Easy to read, clear, concise and easily understandable notes, for people who don't have the time to read through lengthy textbooks. Suitable for Year 1 University students and up, and requires little background understanding.
Description: Easy to read, clear, concise and easily understandable notes, for people who don't have the time to read through lengthy textbooks. Suitable for Year 1 University students and up, and requires little background understanding.