Today we talked about homogeneous 2nd order differential equations. They generally have 2 linearly independent solutions (the linear independence of which can be determined by evaluating the Wronskian). Some methods for solving these equations were presented. If the equation has constant coefficients, or is a Cauchy-Euler equation, then solutions can be found from the corresponding "characteristic equation".
A method was presented for finding the second independent solution of any 2nd order homogeneous ODE, given that a first one has already been found.
Finally, the general solution of nth order linear homogeneous ODE's with constant coefficients was presented.