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    Input/Output Difference Equations

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    Please see the attached file for full problem description.

    These are multiple-choice questions; I only need the correct answers for the three equations

    Find the input/output differential equations for the circuit above when:

    1) y(t) = vR(t)

    2) y(t) = i(t)

    3) y(t) = vC(t)

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    Solution Preview

    Please see the attached file for solutions and explanations.

    The key to solve this question is to write KVL in the given circuit. We have that the loop current is i(t). After writing the KVL equation we will be able to change it in the way that we want for each case:


    Note that we have considered the following equations when writing KVL:

    We should also consider this equation:

    Ok, now we consider each part:

    Solution Summary

    The solution provides detailed steps to reaching the correct of the given equation options for each of the three multiple choice questions posed by the asker.