7. Solution by Undetermined Coefficients

Try these first

1. 1.

   What is the general form of a linear non-homogeneous differential equation?

   Hint

   Look for terms involving y, its first and second derivatives and a function f(x).

2. 2.

   Identify a suitable f(x) for the method of undetermined coefficients.

   Hint

   Think about functions you can easily differentiate or integrate.

3. 3.

   What is a complementary function in the context of differential equations?

   Hint

   Focus on what happens when f(x) = 0.

4. 4.

   Can the method of undetermined coefficients be used for ln(x)?

   • True
   • False

   Hint

   Consider the categories of functions suitable for this method.

5. 5.

   Investigate the differential equation y'' + 2y' + 5y = 10e^x + sin(2x). Provide the general solution.

   Hint

   Pay attention to the form of each term to set up your trial solutions.

6. 6.

   Given the equation y'' - 3y' + 2y = x*cos(x) + 4e^x, decompose the problem into finding complementary and particular solutions, and combine them.

   Hint

   Keep track of your trials—f(x) will provide hints for the forms.