I don't really get what I am meant to be doing here, ALSO (...)- ANYTHING inside brackets are subscripts since I don't know how to do that here. Solve the following first order difference eqn : $$2\,x_{n+1} + 3\,x_n = 0$$ I know the answer is X(n)=A[-3/2]^n (sorry gave you the wrong answer must have confused you my bad!
I have worked it out
$$2\,x+3=0\quad X_n=A\left(-\frac 32\right)^n$$
$$2\,x=-3$$
$$x=-\frac 32$$
and the formula $x_n=C.[a^n]$ but I actually don't really know or understand what I am doing :(
this will probably seem very easy to most of you mathematicians out there but could you please explain every single step?
The basic idea is to assume that any solution has the form $$ x_n = n^kz^n $$ for some $z$. For a particular choice of $k$, that turns the (homogenous) equation into a polynomial in $z$, and the roots of the polynomial thus correspond to the solutions of your difference equation.
You always start with $k=0$, i.e. $x_n = z^n$, and only needs to consider higher values of $k$ if that doesn't yield "enough" solutions.