Variation of Parameter for Variable Coefficient Equation

I just need the one question on first page of the attached pdf solved. Please clearly list and justify each step in words with proper mathematical terminology and notations. Please double check the steps and answer once done.

The rest of the pages in the pdf are relevant textbook explanations and examples for reference.

Answer

Answers can be viewed only if
  1. The questioner was satisfied and accepted the answer, or
  2. The answer was disputed, but the judge evaluated it as 100% correct.
View the answer

1 Attachment

The answer is accepted.