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    Differential equation solved with variables separable method

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    Let x: [0, infinity) -> R and y: [0, infinity) -> R be solutions to the system of differential equations:

    x' = - x

    y' = - sin y

    With initial condition:

    x(0) = y(0) = alpha, where alpha belongs to [0, pi)

    (a) Show that |x(t)| =< alpha for all t >= 0

    (b) Show that | y(t) - x(t) | =< alpha( 1 - e^-t) for all t >= 0. ( e here is exponential function)

    Please justify every step and claim, and if you use any theorems refer to them.

    © BrainMass Inc. brainmass.com March 4, 2021, 6:44 pm ad1c9bdddf
    https://brainmass.com/math/ordinary-differential-equations/differential-equation-solved-variables-separable-method-59710

    Solution Summary

    A given differential equation with initial conditions is solved using variables separable method.

    $2.49

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