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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