For which of the cases below do the given functions form a fundamental set of solutions of the corresponding differential equation on the indicated interval? (i) y" – 7y' + 10y = 0; 5ex, 10e3*, (-∞, 0) (ii) y" – 6y' + 9y = 0; 5e³x, 4xe7*, (-∞,0) (iii) x²y" – 20xy' + 110y = 0; 2x10, &x!º, (0, ∞)
For which of the cases below do the given functions form a fundamental set of solutions of the corresponding differential equation on the indicated interval? (i) y" – 7y' + 10y = 0; 5ex, 10e3*, (-∞, 0) (ii) y" – 6y' + 9y = 0; 5e³x, 4xe7*, (-∞,0) (iii) x²y" – 20xy' + 110y = 0; 2x10, &x!º, (0, ∞)
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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Question
![For which of the cases below do the given functions form a
fundamental set of solutions of the corresponding differential
equation on the indicated interval?
(i) y" – 7y' + 10y = 0; 5ex, 10e5x, (-∞, ∞)
(ii) y" – 6y' + 9y = 0; 5e³x, 4xe7*, (-∞, ∞)
0; 5e3x, 4xe7*,
(-∞, 00)
|
(iii) x²y" – 20xy' + 110y = 0; 2x10, 8x1º, (0, ∞)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F949f7a1f-f6d1-44e7-b99b-2b0ff023989b%2Ffff8948d-d2a4-4570-a1ba-9322d5d04e02%2F802yhao_processed.png&w=3840&q=75)
Transcribed Image Text:For which of the cases below do the given functions form a
fundamental set of solutions of the corresponding differential
equation on the indicated interval?
(i) y" – 7y' + 10y = 0; 5ex, 10e5x, (-∞, ∞)
(ii) y" – 6y' + 9y = 0; 5e³x, 4xe7*, (-∞, ∞)
0; 5e3x, 4xe7*,
(-∞, 00)
|
(iii) x²y" – 20xy' + 110y = 0; 2x10, 8x1º, (0, ∞)
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