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    Solving Second Order Linear Differential Equation by Using D-operator

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    Use D-operators to find a particular solution to the differential equation:
    y^n + y' - 2y= e^-2x

    Hence write its general solution. Find the solution that satisfies the initial conditions:
    y(0) = 1/3, y'(0) = -1/3

    © BrainMass Inc. brainmass.com December 24, 2021, 11:31 pm ad1c9bdddf
    https://brainmass.com/math/ordinary-differential-equations/solving-second-order-linear-differential-equation-d-operator-576598

    SOLUTION This solution is FREE courtesy of BrainMass!

    Solution:
    The characteristic equation is

    so the complementary solution will be

    Given

    Let f(D) =
    Since f(-2) = 0
    f'(D) = 2D+1
    f'(-2) = 2(-2)+1 = -3

    So particular integral will be

    so the general solution will be

    Given y(0) = 1/3

    Now,
    Given y'(0) = -1/3

    Subtract equation (ii) from equation (i)
    3c1 = 1/3
    c1 = 1/9

    Thus, general solution will be

    Answer:

    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-d-operator-576598

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