The given differential equation has a regular singular point at x = 0 .

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Answer 1

Question

Chapter 5.5, Problem 5P

(a)

To determine

To show: The given differential equation has a regular singular point at x=0.

(b)

To determine

The indicial equation, the recurrence relation and the roots of the indicial equation.

(c)

To determine

The series solution x>0 corresponding to the larger root.

(d)

To determine

The series solution for the smaller root if roots are unequal.

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Solve the linear system of equations attached using Gaussian elimination (not Gauss-Jordan) and back subsitution. Remember that: A matrix is in row echelon form if Any row that consists only of zeros is at the bottom of the matrix. The first non-zero entry in each other row is 1. This entry is called aleading 1. The leading 1 of each row, after the first row, lies to the right of the leading 1 of the previous row.

7. Show that for R sufficiently large, the polynomial P(z) in Example 3, Sec. 5, satisfies the inequality |P(z)| R. Suggestion: Observe that there is a positive number R such that the modulus of each quotient in inequality (9), Sec. 5, is less than |an|/n when |z| > R.

9. Establish the identity 1- 1+z+z² + 2n+1 ... +z" = 1- z (z1) and then use it to derive Lagrange's trigonometric identity: 1 1+ cos cos 20 +... + cos no = + 2 sin[(2n+1)0/2] 2 sin(0/2) (0 < 0 < 2л). Suggestion: As for the first identity, write S = 1+z+z² +...+z" and consider the difference S - zS. To derive the second identity, write z = eie in the first one.

Answer 2

Question

Chapter 5.5, Problem 5P

(a)

To determine

To show: The given differential equation has a regular singular point at x=0.

(b)

To determine

The indicial equation, the recurrence relation and the roots of the indicial equation.

(c)

To determine

The series solution x>0 corresponding to the larger root.

(d)

To determine

The series solution for the smaller root if roots are unequal.

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Answer 3

Question

Chapter 5.5, Problem 5P

(a)

To determine

To show: The given differential equation has a regular singular point at x=0.

(b)

To determine

The indicial equation, the recurrence relation and the roots of the indicial equation.

(c)

To determine

The series solution x>0 corresponding to the larger root.

(d)

To determine

The series solution for the smaller root if roots are unequal.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 5.5, Problem 5P

(a)

To determine

To show: The given differential equation has a regular singular point at x=0.

(b)

To determine

The indicial equation, the recurrence relation and the roots of the indicial equation.

(c)

To determine

The series solution x>0 corresponding to the larger root.

(d)

To determine

The series solution for the smaller root if roots are unequal.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 5

Chapter 5.5, Problem 5P

(a)

To determine

To show: The given differential equation has a regular singular point at x=0.

(b)

To determine

The indicial equation, the recurrence relation and the roots of the indicial equation.

(c)

To determine

The series solution x>0 corresponding to the larger root.

(d)

To determine

The series solution for the smaller root if roots are unequal.

Answer 6

Chapter 5.5, Problem 5P

(a)

To determine

To show: The given differential equation has a regular singular point at x=0.

Answer 7

Chapter 5.5, Problem 5P

(a)

To determine

To show: The given differential equation has a regular singular point at x=0.

Answer 8

(b)

To determine

The indicial equation, the recurrence relation and the roots of the indicial equation.

Answer 9

(b)

To determine

The indicial equation, the recurrence relation and the roots of the indicial equation.

Answer 10

(c)

To determine

The series solution x>0 corresponding to the larger root.

Answer 11

(c)

To determine

The series solution x>0 corresponding to the larger root.

Answer 12

(d)

To determine

The series solution for the smaller root if roots are unequal.

Answer 13

(d)

To determine

The series solution for the smaller root if roots are unequal.

Answer 14

Expert Solution & Answer

Answer 15

Expert Solution & Answer

Answer 16

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Answer 17

The given differential equation has a regular singular point at x = 0 .

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To show: The given differential equation has a regular singular point at x=0.

The indicial equation, the recurrence relation and the roots of the indicial equation.

The series solution x>0 corresponding to the larger root.

The series solution for the smaller root if roots are unequal.

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