No, you do not guess solutions with Variation of Parameters as you do with Undetermined coefficients.

Here's the method of Variation of Parameters:

Given a differential equation of the form: having homogeneous solutions and , we assume, by the method of Variation of Parameters, that a particular solution exists of the form:

where and are found from the system of equations:

...............(1)

...............(2)

since and are knowns, we can find the values of and by Cramer's Rule, and then integrate them to get and

then as always, our general solution is given by:

Most textbooks, including your own, condenses this whole method into a single formula involving an integral, look it up if you can't bother with Cramer's rule