Share
Explore BrainMass

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?

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.

$2.19