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    Differentiation : Radius of Convergence for Power Series

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    Consider the differnetial equation
    y'(x) + xy(x) = 0 with y(0) = 0

    Look for a solution of this problem of the form
    y(x) = A + B + Ce^-x + De^-1/2x^2

    Use the fact that y must satisfy the equation and the initial conditions to identify the constants A,B,C and D. By setting u = -x^2/2 in the power series for f(u) = exp{u}, determine a power series for y(x). What is the radius of convergence of the power series for y(x)?

    I am having trouble in grasping the whole concept of this problem. Can anyone help?

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    https://brainmass.com/math/basic-algebra/differentiation-radius-convergence-power-series-18808

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    Consider the differnetial equation
    y'(x) + xy(x) = 0 with y(0) = 0

    Look for a solution of this problem of the form

    Use the fact that y must satisfy the equation and the initial conditions to indentify the constants A,B,C and D. By setting u = -x^2/2 in the power series for
    f(u) = exp{u}, determine a power series for y(x). What is the ...

    Solution Summary

    A radius of convergence for a power series is found. The solution is detailed and well-presented.

    $2.19

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