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Numerical Integration and Euler's Formula

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For this question, please leave out the proof. Assume the formula is already known.

Also, instead of assuming a unit step of U(t) = 1(t), change the question to a sinusoidal input of U(t) = sin(2t).

Please solve this question and explain all the steps in detail.

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Solution Summary

The solution provides a calculation involving Euler's formula as well as a simple proof for the formula.

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For the equation you had provided for the modified Euler formula, I have now figured out what the general form of the differential equation is:

dx/dt = ax + bu = f(x,t)

Then the modified Euler formula is,

x(n+1) ...

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