I've been thinking about this for a while now and am making.. some.. headway
1. Since R=0 there would be no 1st derivative term and since E is a constant, its derivative would just be 0, it would just be:
So would I just continue and solve like a regular 2nd order DE?
but then where would the 1/LC come in?
2. Same thing with R=0 but the right side would have a cosine instead? or an (alpha)cosx?