Hello everybody,

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:

real:and

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:

or

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,

SkyWolf.