solve using variation of parameters:

y"+36y=[csc(6t)]^2

I don't understand variation of parameters very well at all.

go to wolframalpha . com and type in the box:

solve y"+36y=[csc(6t)]^2

It will show the solution. If you then click on the "Show Steps" button, it will explain the solution. Study that, along with your class materials and several excellent online articles, and it should become clearer. If not, you'l probably need some in-person help.