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

 

 

On to Lesson 33 - Area Between Two Curves

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