Undetermined coefficients, part 2

Lesson 6F

What should the particular solution look like?

Most of the work when using the method of undetermined coefficients is centered around finding the coefficients.

Before you can find the coefficients, you need to know what the particular solution looks like. Here is how you do that.

Use what you learned in the video to figure out what the particular solution to these two differential equations looks like: \[ y''+y’+100y = 9t^3 \] \[ y'' + y’ + 100 y = \sin 2t + \cos t \]

Although I personally think using charts to find the particular solution is more confusing, there is one in the book on page 181.

Bumping up

You need to make sure that no piece of the the particular solution is a solution to the homogeneous version of the differential equation.