i'm really stuck with this and i hope somebody can help me out.
I have this differential equation:
sadly there is no further explaination on what i should do with the parameter, so here is how i got through:
i wrote the omogeneous equation:
then tried to find its general solution by writing the characteristic equation:
which has the following zeroes:
complex:Which leads to the general solution of the omogeneous equation.
Now, on to the parameter; due to the fact that the coefficient, correct me if i'm wrong, changes the way my particular solution of the complete equation is wrote, should i study the cases where equals the characteristic equation zeroes? And if this is the right procedure, when i study the case in which:
my solution will have the complex exponent?
Such as: ?
Hope this is a clear enough question, excuse me for my poor english
and thanks in advance,