I think i'm understanding it, but there's just something else that's puzzling.
We have:
and we're comparing this with:
Comparing coefficients we get:
and
Is this equal to:
and
?
For the next part:
This gives:
and since the -2 on the LHS does not contain a t then there is no value of
for which this is true.
Correct
I haven't tried it with the y's yet since it has to satisfy both these conditions to be homogeneous. Since this one doesn't work the DE is non-homogeneous.
Correct. You will end up with the same situation with the y's, where there is no value where this would be true.
Is that about right?