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1.] For the given differential equation, X=U is a/an: A. Regular point B. Ordinary point C. Regular singular point D. Irregular singular point 2. Which of the following is the correct form for the solution y? 100 A.y = 1 anx-r B.y = ax+r +7=0 C. y = Σn=0 anx 00 D.y = Σn=1 anx" 3. The indicial equation for the given differential equation is: A. r(r-4)= 0 B. r(2r + 1) = 0 C. r(r-3) = 0 D. None of these/Not applicable

1.] For the given differential equation, X=U is a/an: A. Regular point B. Ordinary point C. Regular singular point D. Irregular singular point 2. Which of the following is the correct form for the solution y? 100 A.y = 1 anx-r B.y = ax+r +7=0 C. y = Σn=0 anx 00 D.y = Σn=1 anx" 3. The indicial equation for the given differential equation is: A. r(r-4)= 0 B. r(2r + 1) = 0 C. r(r-3) = 0 D. None of these/Not applicable

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Part 1. Obtain a solution to the following differential equation valid near the origin: 1.] For the given differential equation, x = 0 is a/an: A. Regular point B. Ordinary point y"+3xy' +7y=0 C. Regular singular point D. Irregular singular point 2. Which of the following is the correct form for the solution y? 100 A. y = E=1 anxn-r B.y = no anx+r 100 C. y = Σn=0 anx D.y = Σn=1 anx¹ 3. The indicial equation for the given differential equation is: A. r(r-4)= 0 B. r(2r + 1) = 0 C. r(r-3) = 0 D. None of these/Not applicable 4. The recurrence relation for n ≥ 2 is: A. n(n-1)an + (3n+ 1)an-2 = 0 B. n(n-1)an + (3n+7)an-2 = 0 C. n(n+1)an-2 + (3n+ 1)an = 0 D. n(n+1)an-2 + (3n+ 7)an = 0
Transcribed Image Text:Part 1. Obtain a solution to the following differential equation valid near the origin: 1.] For the given differential equation, x = 0 is a/an: A. Regular point B. Ordinary point y"+3xy' +7y=0 C. Regular singular point D. Irregular singular point 2. Which of the following is the correct form for the solution y? 100 A. y = E=1 anxn-r B.y = no anx+r 100 C. y = Σn=0 anx D.y = Σn=1 anx¹ 3. The indicial equation for the given differential equation is: A. r(r-4)= 0 B. r(2r + 1) = 0 C. r(r-3) = 0 D. None of these/Not applicable 4. The recurrence relation for n ≥ 2 is: A. n(n-1)an + (3n+ 1)an-2 = 0 B. n(n-1)an + (3n+7)an-2 = 0 C. n(n+1)an-2 + (3n+ 1)an = 0 D. n(n+1)an-2 + (3n+ 7)an = 0
5. Which of the following is the expression for a2k in terms of a? A. azk= (-1) [10-16-22---(6k+4)] (2k+1)! (-1)k[7-13-19 (6k+1)] (2k)! (−1)k[6-12-18---(6k)] (2k+1)! B. azk= C. azk= D. azk= A. azk+1 = (-1)k[8.14-20(6k+2)] (2k)! B. azk+1 = C. a₂k+1 = -ao ao 6. Which of the following is the expression for a2k+1 in terms of a₂? D. azk+1 = ·ao ao (2k)! (-1) [6-12-18 (6k)] (2k+1)! (-1) [10-16-22-(6k+4)] (2k+1)! (-1) [7-13-19--(6k+1)] -a₁ (-1) [8-14-20-(6k+2)] (2k)! a₁ a₁ a₁
Transcribed Image Text:5. Which of the following is the expression for a2k in terms of a? A. azk= (-1) [10-16-22---(6k+4)] (2k+1)! (-1)k[7-13-19 (6k+1)] (2k)! (−1)k[6-12-18---(6k)] (2k+1)! B. azk= C. azk= D. azk= A. azk+1 = (-1)k[8.14-20(6k+2)] (2k)! B. azk+1 = C. a₂k+1 = -ao ao 6. Which of the following is the expression for a2k+1 in terms of a₂? D. azk+1 = ·ao ao (2k)! (-1) [6-12-18 (6k)] (2k+1)! (-1) [10-16-22-(6k+4)] (2k+1)! (-1) [7-13-19--(6k+1)] -a₁ (-1) [8-14-20-(6k+2)] (2k)! a₁ a₁ a₁
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