ok. so i am given an equation.

y''+4y=12x

i am told that the a particular equation is : y=3x

i understand that, it makes the first function =0. i know how to do that.

but then i am given the complimentary function as y=c1cos(2x)+c2sin(2x)

so my question is, where does that come from? how could i have found that on my own? i have a test and i believe our professor mentioned that we wouldn't be given those as we have been in our homework sets, so i need to be capable of finding it just from

y''+4y=12x.

i don't know how though. i did figure the particular one out, but this i am stuck.