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
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Chapter2: Second-order Linear Odes
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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, ∞)
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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