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    Solving Second Order Linear Differential Equation

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    Find the transient and steady-state currents in the RLC circuit with L= 5 henrys, R= 10 ohms, C=0.1 farad and E=25sint volts.
    L(d^2Q/dt^2) + R(dQ/dt) + 1/C*Q = E refer to attachment for better formula representation.

    © BrainMass Inc. brainmass.com December 24, 2021, 11:31 pm ad1c9bdddf
    https://brainmass.com/math/ordinary-differential-equations/solving-second-order-linear-differential-equation-576679

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    SOLUTION This solution is FREE courtesy of BrainMass!

    Solution:
    The differential equation will be

    The characteristic equation is

    so the complementary solution will be

    This is called transient part of the solution.
    Let particular solutions be

    This gives
    A+2B = 0
    -2A + B = 5
    After solving, we will get
    B = 1, A = -2
    Thus,
    This is called steady state term of the solution.
    The general solution is

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 11:31 pm ad1c9bdddf>
    https://brainmass.com/math/ordinary-differential-equations/solving-second-order-linear-differential-equation-576679

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