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SECTION 2.2 SEPARABLE EQUATIONS
We know how to solve ﬁrst order linear ordinary diﬀerential equations. What about ﬁrst
order
non
linear ordinary diﬀerential equations? If we use
x
as the (independent) variable,
then we want to consider
dy
dx
=
f
(
x,y
)
.
In general we won’t know how to solve such a thing. But there are some important special
cases.
Separable equations.
If we can do some algebra and rewrite the equation in the form
S
(
y
)
dy
dx
=
R
(
x
)
,
then we can (?) just integrate both sides! Equations for which we can do this are called
separable.
NOTES.
As always, integration may be a problem. Solving explicitly for
y
may also be
a problem, but when we can do it, we should. Sometimes we treat
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 Spring '08
 Fonken
 Differential Equations, Equations

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