I've come across some notation that I've never had to deal with, so I'm not to sure what I'm supposed to do.

I have an equation

I'm supposed to show by direct substitution that the displacement satisfies the differential equation

I'm really thrown off by the term 'direct substitution' as we haven't used it in this unit. What am I supposed to substitute into what??

Also, the notation of is confusing me too - what is this in relation to?

Also, please, no giving me answers to the equation, I'm moreso after an explanation of what I'm supposed to be doing here...