As you work through WeBWorK #9, you may run into a few instances where it is not obvious what guess to make for the particular solution to the nonhomogeneous equation. Here are two tips that might help:
What if the right side has both an exponential and a trig function?
If the right side of your differential equation has form similar to:
then your guess should have the form:
What if the right side is a solution to the complementary equation (where the complementary equation has a repeated root)?
If your initial guess: is a solution to the complementary equation, we adjust it by multiplying by : .
If is *also* a solution to the complementary equation (due to a repeated root), adjust it by multiplying by again: .
Let me know if you run into other weird things. Questions are natural, and welcome!