Calculus
Lesson
32
DEs
- Separation of Variables
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we've already covered getting ys and xs on their own sides:
Examples:
If you can't separate variables, you must check to see if you
can change variables:
Definition: if the equation is:
then if
,
we call the DE a HOMOGENEOUS equation of degree n.
Example:
If a DE is homogeneous, we can separate the variables with a variable change!
Steps to changing variables:
1) try to separate variables first!
2) check to see if the DE is homogeneous
3)
substitute
. Remember that
4)
separate
and
5) solve
6)
back-substitute
7)
in particular,
solve for
Examples:
both in general and
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