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