6.3.1. Method of Undetermined Coefficients

Try these first

1. 1.

   What is the first step in the Method of Undetermined Coefficients?

   Hint

   Think about what f(x) looks like.

2. 2.

   When do you need to modify your guessed solution for y_p?

   Hint

   What do we call a solution that has the same terms?

3. 3.

   What type of functions can f(x) be in the Method of Undetermined Coefficients?

   • Only polynomials
   • Polynomials
   • exponentials and trigonometric functions
   • Any function

   Hint

   Recall the conditions of application for this method.

4. 4.

   True or False: The guessed y_p should always be different from y_h in form.

   • True
   • False

   Hint

   Consider what independence means in this context.

5. 5.

   Solve the non-homogeneous differential equation d²y/dx² + 3dy/dx + 2y = e^(-x)sin(x) using the Method of Undetermined Coefficients.

   Hint

   Consider the overlap and adjust your guess accordingly.

6. 6.

   For the equation d²y/dx² - 4y = 3x + 2, apply the Method of Undetermined Coefficients to find the general solution.

   Hint

   Pay attention to the linear terms when you substitute.