Recall that a rst order linear di erential equation is an equation which can be written in the form y + p(x)y = q(x) where p and q are continuous functions on some interval i. A second order linear di erential equation has an analogous form. The functions p and q are called the coe cients of the equation; the function f on the right-hand side is called the forcing function or the nonhomogeneous term. The term forcing function comes from the applications of second-order equations; an explanation of the alternative term nonhomogeneous is given below. A second order equation which is not linear is said to be nonlinear . Remarks on linear. an operator that transforms a twice di erentiable function y = y(x) continuous function. Set l[y] = y + p(x)y + q(x)y. L[y(x)] = y (x) + p(x)y (x) + q(x)y(x), 39 then, for any two twice di erentiable functions y1(x) and y2(x),
