1.7.2. Method of Variation of Parameters

Try these first

1. 1.

   What is the method of variation of parameters used for?

   Hint

   Think about equations that can't use simpler methods.

2. 2.

   In variation of parameters, what do we replace the constants with?

   Hint

   Recall the expression for the complementary solution.

3. 3.

   What does the method of variation of parameters specifically address?

   • Homogeneous equations
   • Non-homogeneous equations
   • Special cases only

   Hint

   Consider what differentiates non-homogeneous from homogeneous equations.

4. 4.

   True or False: The functions u_1 and u_2 are constants in the variation of parameters method.

   • True
   • False

   Hint

   Think about how we construct the particular solution.

5. 5.

   Use the method of variation of parameters to solve the equation y'' - 4y' + 4y = e^(2x). What steps will you take to arrive at the final solution?

   Hint

   Be sure to differentiate and set up your system correctly.

6. 6.

   Consider the equation y'' + y = tan(x). Utilize the method of variation of parameters to describe how you would find the particular solution.

   Hint

   Pay close attention to the trigonometric identity when working with tangent.