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    Differential Equations

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    (i) Consider the differential equation:
    x. = x^2 , x(0) given x(0)>0

    Find the solution of x(t) of this equation in terms of x(0) and show that there is a T, which depends on x(0), such that lim x(t) = infinity t --> T-

    (ii) Find the solution of the differential equation
    x.. - x = e^-t/2 , x(0) = 0, (0) = 1,
    Using the reduction of order method.

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    https://brainmass.com/math/calculus-and-analysis/differential-equations-reduction-order-methods-6190

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    Solution. (1) From x'=x^2, we have
    dx/dt=x^2
    Then 1/x^2dx=dt.
    Integrate both sides to get
    -1/x=t+C,
    where C is a constant. According to the initial condition we know that, when t=0, x=x(0)>0. So C=-1/x(0). The ...

    Solution Summary

    Two differential equations are solved. The differential equations for reduction of order methods are determined. Limits that go to infinity are given.

    $2.19

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