Guessing the particular integral. PLEASE HELP

For an assignment on my maths uni course, I have been asked in each case below, to give the particular integral which you should try, in a format that includes unknown constants. I am not required to do any working or substitution, just give the particular integral guess. Any help would be greatly appreciated.

a) h(t)=sin3t
b) h(t)=e^t
c) h(t)=e^t (sin6t)
d) h(t)=e^4t (sin3t)
e) h(t)=e^t (sin3t)
f) h(t)=5e^t (cos3t)

What do you think? Don't you have any notes on this?

For example, the first one would be $A\cos(3t) + B \sin(3t)$.

I have a few notes. for example, I think that as you say, the first would be x=Csin3t + Dcos2t, and for part b) I think it would be x = Ce^t. However, I haven't been given any notes on what to do when you have an exponential and a trigonometric part combined.

Have an educated guess. Hint: it's a combination of both P.I's.

Would d) be x = Ae^4t(sin3t) + Be^4t(cos3t) ???

Yep, so you can leave it as $e^{4t}(A\sin 3t + B\cos 3t)$ for simplicity.

Fantastic. Does it change at all for f) given the 5 before the function? I'm assuming it doesn't affect the particular integral.

That doesn't matter.