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    Homogeneous, Particular, and General Solutions

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    Y''(t) + 6y'(t) + 13y(t) = te^(-t)
    Compute the homogeneous solution yh(t).
    Compute the particular solution yp(t).
    Compute the general solution y(t) if y(0)=0 and y'(0)=1/8

    © BrainMass Inc. brainmass.com November 24, 2022, 11:52 am ad1c9bdddf

    Solution Preview

    Homogeneous Solution:

    Aux. equation is: m^2 + 6m +13 = 0
    m = (1/2)[-6 (+/-) sqrt(36-52) = -3 (+/-) i2

    Two complex roots, m1 = -3+i2 and m2 = -3-i2

    Hence, the homo. solution is:

    yh(t) = e^(-3t) * [C1*Cos 2t + C2*Sin 2t]

    Particular Solution:

    Forcing function = te^(-t)
    So, solution should ...

    Solution Summary

    The solution explains clearly and concisely the calculations necessary to reach the homogeneous, particular and general solutions of the given equation.