I understand how to solve a normal second order linear equation, but this question in the homework is a bit more theoretical and I'm a bit confused. "Suppose y1(t) and y2(t) are solutions of y'' + py' + qy = 0 Verify that y(t) = k1y1(t) + k2y2(t) is also a solution for any choice of constants k1 and k2." If we were given actual functions (i.e. e^-t) this would be very simple. Just plug it into the DE and see that you have an equality. But when given arbitrary functions I dont know how to verify that its an equality. Im guessing it has something to do with the Linearity Principle, but I dont understand how to actually verify it.