6. Find a particular solution yp(x) of
y''(x) - y(x) = x + 3

Can someone help me on how to solve these types of problems??

This is what I am doing..
for a particular solution, i know
Yp(x)=Ax+B in this case.
so i take derivative twice....
Y'p(x)=A
Y''p(x)=0

I plugged into equation and got,
Ax+B=x+3.... not sure where to go from here..
but am i even doing this right??

Any help will be greatly appreciated! thanks!!!

You're doing things right.
but y''(x) - y(x) = 0 - (Ax+B) = -Ax - B

so : -Ax - B = x + 3

those 2 linear functions are equal, this means that their coefficients are equal each with the other :
-A = 1
-B = 3

A = -1
B = -3

Particular solution is : y(x) = -x - 3

Do you need help also for the general solution ?