Book pages at https://books.google.co.in/books?id=d-7owi6uNtMC
What I see is that they have taken d^2 v/dt^2 as an input at point A, integrated it to get dv/dt, integrated it again to get v=2sin3t V, and then inverted the output to get -9v gain. But this makes the feedback input as (-9)(2sin3t) and not double derivative to keep an undamped sine wave as output. The previous assumed double derivative as input is not what is given as feedback to have a sustained sine wave ?
source and problem in : Engineering circuit analysis by Hayt