MA 36600 LECTURE NOTES: FRIDAY, JANUARY 16
3
If we did not keep track of the initial condition
y
(0) =
y
0
, we would call the solution of the di
ff
erential
equation alone the
general solution
. For example,
y
(
t
) = (
b/a
) +
C
1
e
at
would be the general solution for the
di
ff
erential equation above because it involves an arbitrary constant
C
1
. If we do keep track of the initial
condition, we would call the solution the
particular solution
. For example,
y
(
t
) = (
b/a
)+(
y
0
−
b/a
)
e
at
would
be the particular solution corresponding to
y
(0) =
y
0
.
Classification of Differential Equations
Types of Di
ff
erential Equations.
There are two:
•
ODEs
or
ordinary di
ff
erential equations
are di
ff
erential equations which do not involve partial deriva
tives.
•
PDEs
or
partial di
ff
erential equations
are di
ff
erential equations which do involve partial derivatives.
Each of the examples of di
ff
erential equation we have seen are types of ODEs, so here is an example of a
PDE: Say that we have a rod of length
L
sitting in or above a heat source. (For example, the rod might have
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 Spring '09
 EdrayGoins
 Differential Equations, Derivative, Partial differential equation

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