For each of these choices of F in Newton's second law (1.8), classify (1.8) as a linear

Question:

For each of these choices of F in Newton's second law (1.8), classify (1.8) as a linear or nonlinear differential equation (a, b, c, and k are constants).
(a) F = c;
(b) F = -kx;
(c) F = -ax3;
(d) F = b sin ax;
(e) F = a - kx.
[Classical-mechanical systems that show chaotic behavior (Section 1.4) obey nonlinear differential equations, but not all nonlinear differential equations give rise to chaotic behavior.]