MATH 33B Study Guide - Equilibrium Point, Constant Function, Integral Curve
Document Summary
Di erential equations and solutions: an ordinary di erential equation (ode) is an equation involving a func- tion y of one variable t and various derivatives of y, (cid:16) t, y, y(cid:48), . = 0: the order of a di erential equation is the order of the highest order deriva- tive, an ode can be put into normal form by solving for the highest order derivative, (cid:16) t, y, y(cid:48), . , y(n 1)(cid:17) y(n) = f: a solution to an nth-order ode is an n-times continuously di erentiable function which satis es the equation. Consider the rst-order ode and the family of functions y(cid:48) = ty y(t) = cet2/2, where c is a constant. Since y(cid:48)(t) = tcet2/2 = ty(t), the functions y(t) are solutions of the equation. Specifying an initial condition, for example, y(2) = 10, will specify a unique solution.
