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