1. Decide whether the following operators are linear or not:

a.) The operator D_2, which take any twice-differentiable function f to f", its second derivative.

b.) The operator R, which takes any non-zero function f to it's reciprocal 1/f

2.

Say that the auxiliary equation of ??????+?????+????=0 has distinct real roots. Find the solution of ??????+?????+????=0,??(??0)=??0,???(??0)=??1

6.) Decide whether the following operators are linear or not: a.) The operator D2, which take any twice-differentiable function f to f\1.) Say that the auxiliary equation of ay" + by' + cy = 0 has distinct real roots. Find the solution of ay" + by' + cy = 0, y(xo) = ko, y'(xo) = k1