Sorry if this is a stupid question, but I'm taking a differential equations course this semester, and was wondering something about initial value problems. For first order linear equations, when given an initial value problem, we were given an initial condition, such as y(0) = 1. For 2nd and higher order differential equations, why is it that initial conditions always seem to be given as y(0) = 1, y'(0) = 1 etc.? Would it be enough just to specify y at two different places, i.e. y(0) = 1 and y(2) = 5 or is that not always the case? Thanks a lot for any explanation.