The CF will be your trial solution should be
I need help with the first part mostly!
for the associated homogeneous
D = d/dx
roots a = b = i
when you sub it into the homogeneous, the real parts cancel but the imaginary doesn't!
I was wondering why this is?
Am i right in thinking the trial solution is wrong?
For the particular solutions of the other parts I got
please verify these!
When you have a complex conjugate pair (i and -i) of roots, then you use the cosine and sine functions. In your case, the solution to the homogeneous equation is .
Your particular solution for is incorrect. Try .