Question

In: Advanced Math

Determine a lower bound for the radius of convergence of series solutions about each given point...

Determine a lower bound for the radius of convergence of series solutions about each given point x0 for the given differential equation.

(1 + x^3)y'' + 4xy' + 6xy = 0

x0 = 0. x0 = 4

Solutions

Expert Solution

Solution:-

Given that

or,

Here and and

p(x) and q(x) has singular point when

For,

Distance from 0 to -1 is | (-1 - 0)| = 1

and distance in the complex domain from to is

The lower bound for the radius of convergence of series solution about is 1

lower bound for is 1.

For

The distance from 4 to -1 is |4 - (-1)| = 5

The distance in the complex domain from 4 to is

and min is

Lower bound for is

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Colby Messinger answered 1 year ago

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