Many problems are assigned because this section is the foundation of much of the remaining material in the course. It is therefore important that you master the material in this section. Do the problems immediately because the next two sections (and Ch. 5) depend entirely on this section.

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THIS IS AN EXTREMELY IMPORTANT SECTION.

NEARLY EVERYTHING WE DO HEREAFTER DEPENDS ON THIS SECTION.

IT'S IMPORTANT THAT YOU MASTER THIS SECTION.

To check your work, use Maple's factor command to factor your characteristic equations, or use Maple's solve command to solve your characteristic equations for m. For review on Maple's factor and solve commands, go to the Maple Help Sheets and click on the first tutorial called "Basics" and the second tutorial entitled "Solution of Equations."

Also see the handout on factoring polynomials by synthetic division.
NOTE: Some polynomials can be factored easily without synthetic division!

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STUDY THE EXAMPLES AT THE BOTTOM OF THIS PAGE.
I worked Examples 1 – 6 in class. You should study Ex. 7.

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Do these problems after Friday's lecture.
• 1 – 13 odd,

• 29, 31, 33, 34, 37, 39
  Answer to 34:   y = 5e^x + 5xe^x
  Do these problems after Monday's lecture:

• 15 – 27 odd, 24,
  Answer to 24:   y = c₁e^x + c₂xe^x + c₃e^–x + c₄xe^–x

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Summary: The entire assignment for the section is:

• 1 – 33 odd,

• 24, 34, 37, 39

Answer to 24:   y = c₁e^x + c₂xe^x + c₃e^–x + c₄xe^–x

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Also see these examples:

1. Example 1
2. Example 2
3. Example 3
4. Example 4
5. Example 5
6. Example 6
7. Example 7

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