Question

True or False? Justify your answer with a proof or a counterexample. You can determine the behavior of all first-order differential equations using di

Differential equations
ANSWERED
asked 2021-07-05
True or False? Justify your answer with a proof or a counterexample. You can determine the behavior of all first-order differential equations using directional fields or Euler's method.

Expert Answers (2)

2021-07-06
Yes certainly, because you can determine the behavior of the solutions using the directional fields which give you where the stable, unstable and semi-stable solutions, shows the initial condition on it the solutions behaviors depend.
And by Euler method you can get too close numerical solution by decreasing the step you use
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Best answer
2021-07-29

The Euler method is a first-order method, which means that the local error (error per step) is proportional to the square of the step size, and the global error (error at a given time) is proportional to the step size.

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