Not sure what you mean by initial conditions and having a complete statement of the DE.
I don't know what you mean by the general solution the differential equation, I haven't started University and my knowledge of differential equations is limited to first-order differential equations.
For my Physics coursework I'm trying to show how the equation to describe simple harmonic motion, this is where I'm up to now:
t is time;
k is spring constant;
m is mass.
A is an unknown constant;
b is an...