Undetermined coefficients (theory question)

Any time you are given a differential equation with variable coefficients, that means the method of undetermined coefficients is applied, correct? If I am told that I am not being tested on the method of undetermined coefficients, can I neglect studying higher order differential equations that have variable coefficients?

Re: Undetermined coefficients (theory question)

No, the coefficients need to be constant, not a function in terms of the independent variable. The method of undetermined coefficients is a special case method. Even without studying this, you will need to still study higher order differential equations. The variation of parameters method is one example to this.

Re: Undetermined coefficients (theory question)

The "method of undetermined coefficients" will work for **any** linear non-homogeneous differential equation **but** you need to know what kind of functions you apply the coefficients to! Typically, those will be the same as the kinds of functions you get as solutions for the homogeneous equation. That is, for constant coefficients equations, exponentials, sine and cosine, polynomials, and products of those.