7.8. Common Mistakes to Avoid

Try these first

1. 1.

   What should you check before deciding on a trial solution?

   Hint

   Think about the terms that you've already solved.

2. 2.

   Name one common arithmetic error in substitutions.

   Hint

   Recall the importance of accuracy.

3. 3.

   Why is it important to check for duplication with the complementary function?

   • To find the correct derivative
   • To avoid wrong trial solutions
   • To simplify the equation

   Hint

   Think about what happens if you reuse an ingredient in cooking.

4. 4.

   True or False: You should include all terms in your polynomial trial solution.

   • True
   • False

   Hint

   Consider the implications of an incomplete recipe.

5. 5.

   Provide an example of a differential equation where forgetting the domain of validity led to a non-viable solution

   Hint

   Refer back to the conditions specified in the problem description.

6. 6.

   Construct a complex example of a situation where incomplete trial functions incorrectly satisfied the equation. Detail how correction was made.

   Hint

   Think about how polynomials are built from their terms.