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    Solving Linear Homogeneous Differential Equations

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    Consider the differential equation y''-2y'+2y = cost

    (a) Find a general solution to this equation using techniques for solving linear homogeneous differential equations with constant coefficients in combination with a variation of parameters.

    (b) Use Laplace Transforms to solve this differential equation with the initial conditions
    y(0) = 1, y'(0) = 0

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    https://brainmass.com/math/calculus-and-analysis/solving-linear-homogeneous-differential-equations-129376

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    Consider the differential equation y''-2y'+2y = cost

    (a) Find a general solution to this equation using techniques for solving linear homogeneous differential equations with constant coefficients in combination with a variation of parameters.

    Notice that the associated homogenous equation is linear second order with constant coefficients.

    First, we "guess" a homogenous solution in the form:

    Plugging this back into the equation we obtain:

    The roots of the last equation are:

    So the solution is:

    As expected, we get two ...

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