If a differential equation has no analytic solution, that is equivalent to saying that it is chaotic That means that answer c is true, and answer d is false And since only nonlinear systems can be chaotic, answer b is true, and answer a is false ODE solvers on computers generate approximate solutions of ODEs The approximate nature comes from a variety of causes, one of which is that they have finite time steps Another is that they are finite truncations of power series A third reason is that computer arithmetic is imprecise Computers work with finite-precision arithmetic, and so at every step the ODE solver is going to make a small mistake And the answer to this is definitely false