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Chapter 2
Heat Conduction Equation
2116C
A linear homogeneous differential equation of order
n
is expressed in the most general form as
y
f xy
f
xy
nn
()
(
)
++
+
′
+=
−
−
1
1
1
0
L
Each term in a linear homogeneous equation contains the dependent variable or one of its derivatives after
the equation is cleared of any common factors. The equation
is linear and homogeneous
since each term is linear in
y,
and contains the dependent variable or one of its derivatives.
′′
−=
yx
y
4
2
0
0
2117C
A differential equation is said to have
constant coefficients
if the coefficients of all the terms
which involve the dependent variable or its derivatives are constants. If, after cleared of any common
factors, any of the terms with the dependent variable or its derivatives involve the independent variable as a
coefficient, that equation is said to have
variable coefficients
The equation
has variable
coefficients whereas the equation
y
4
2
′′ −
=
yy
40
has constant coefficients.
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This note was uploaded on 01/14/2012 for the course PHY 4803 taught by Professor Dr.danielarenas during the Fall '10 term at UNF.
 Fall '10
 Dr.DanielArenas
 Thermodynamics, Mass, Heat

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