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 diFerential
equation alone the
general solution
. ±or example,
y
(
t
)=(
b/a
)+
C
1
e
at
would be the general solution for the
diFerential 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
. ±or 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 DiFerential Equations.
There are two:
•
ODEs
or
ordinary diferential equations
are diFerential equations which do not involve partial deriva
tives.
•
PDEs
or
partial diferential equations
are diFerential equations which do involve partial derivatives.
Each of the examples of diFerential 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. (±or example, the rod might have
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 Spring '09
 EdrayGoins
 Differential Equations, Derivative, Partial differential equation

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