In the prior section, we saw how to solve DE's and IVP's graphically (by graphing slope fields and sketching in solution curves) and numerically, by using Euler's Method to approximate values of the solution function at specific points.
In this section we'll look at a really simple method to solve DE's algebraically, in terms of x and y.
It would be lovely if this method worked for all first order DE's but, alas, it does not. This method requires that the x's and y's can be separated from each other on each side of the equality.
In the following videos, you'll learn this method, called "Separation of Variables" and also learn to identify when it can and when it cannot be used.
Videos:
Introduction to Separable DE's
Assigned Problems
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Section 8.3 [9.3]: Separation of Variables
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1st Edition page 595
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3rd Edition page 618
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Identify Separable DE’s
Solve Separable DE’s and IVP’s
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2, 3 (#2: yes)
7,9,11, 13, 15,
17, 21, 25
27, 29
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2, 3 (#2: yes)
7, 9, 11, 13, 15
19, 23, 31
33, 35
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