# Differentiation : Radius of Convergence for Power Series

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?

Â© BrainMass Inc. brainmass.com May 24, 2023, 1:22 pm ad1c9bdddfhttps://brainmass.com/math/basic-algebra/differentiation-radius-convergence-power-series-18808

#### Solution Preview

Please see the attached file for the complete solution.

Thanks for using BrainMass.

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.