- #1
Plaetean
- 36
- 0
Homework Statement
Homework Equations
y=yPI+yCF
The Attempt at a Solution
First issue is I was under the impression that a particular solution is the final solution to a DE; a solved DE with initial conditions applied, but it would be weird for that to be the first part of the question so I'm interpreting a) as asking for the particular integral (maybe they're the same thing :S). Anyway for the first part of the question I've done:
yPI=Ceit
so dyPI/dt = iCeit and d2yPI/dt2= -Ceit
-C+4C=1
which gives: C=1/3
so yPI=(1/3)eit
Using a trial solution for the complementary function gives yCF=Ae2it+Be-2it
and a general solution of:
y=Ae2it+Be-2it+(1/3)eit
At this point I have no idea how to start applying initial conditions as I have an expression that's full of 'i's, so maybe I don't understand the first part of the question and have gone about the whole thing the wrong way. Some help would be really appreciated!
Last edited: