Without actually solving the given differential equation, find the minimum radius of convergence R of power series solutions about the ordinary point x = 0. About the ordinary point x = 1. (x2 − 2x + 26)y'' + xy' − 4y = 0

R1= 10.04

R2=10

Step-by-step explanation:

The differential equation is given by:

The minimum radius of convergence is given by the distance from the point x=a, to the nearest singularity points of the differential equation.

The singularity points are the roots of the polynomial that multiplies the second derivative of y. Thus, you have:

the roots are in the complex plane. The radius of convergence is the distance between the points z1=0+0i, z2=1+0i (x=0 and x=1, respectively), in the complex plane, that is:

it's equivalent, so we can say that its equal.

let's call the denominator x and the numerador is 18 less then denominator, x - 18.

multiply

2.x = 5.(x - 18)

2x = 5x - 90

90 = 5x - 2x

90 = 3x

x = 90/3

x = 30

so: