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    Ordinary differential equation

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    Solve the ode y'' - y' +4y = 0 as a system of first order odes.

    © BrainMass Inc. brainmass.com October 9, 2019, 10:17 pm ad1c9bdddf
    https://brainmass.com/math/ordinary-differential-equations/ordinary-differential-equation-example-problem-215011

    Solution Preview

    set x_1 = y and x_2 = y' so that

    x_1 ' = y' and

    x_2 ' = y '' = y ' - 4y = x_2 - 4x_1

    hence the given equation is equivalent to the system

    X ' =

    (0 1)
    (-4 1) X

    where X = [x_1 x_2] is a column vector.

    The eigenvalues of the matrix ...

    Solution Summary

    This provides an example of solving an ordinary differential equation as a system of first-order ordinary differential equations.

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