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Determine a lower bound for the radius of convergence of series solutions about the given point x0 for the differential equation:(x2-2x-3)y"+xy'+4y=0x0=4x0=0

Question

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

(x2-2x-3)y"+xy'+4y=0

  • x0=4
  • x0=0
check_circleAnswer
Step 1

Given:

The differential equation is (x2-2x-3)y”+xy’+4y=0

Step 2

Calculation:

Rewrite the given equation as follows.

(х-3)(х+1)у"+ ху' + 4у 30
4у
ху"
-0
у" +
(х-3)(x+1) (х-3)(*+1)
4
and Q(*) - (x-3)(х+1)
х
where P (x-3)(x +1)
help_outline

Image Transcriptionclose

(х-3)(х+1)у"+ ху' + 4у 30 4у ху" -0 у" + (х-3)(x+1) (х-3)(*+1) 4 and Q(*) - (x-3)(х+1) х where P (x-3)(x +1)

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Step 3

The lower bound of the given function is the minimum distance from r1, r2 and x0, where r1 and r2 are the zeros of the given ...

x-3)(x+1)0
x 3 and x 1
= -1 and r, =3
Thus, the value of
help_outline

Image Transcriptionclose

x-3)(x+1)0 x 3 and x 1 = -1 and r, =3 Thus, the value of

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