In Problems 19-24, use the method of Frobenius to find at least the first four nonzero terms in the series expansion about x = 0 for a solution to the given equation for x > 0. 19. 9x2y" +9x²y' + 2y = 0 20. 2x(x-1)y" + 3(x-1)y' - y = 0
In Problems 19-24, use the method of Frobenius to find at least the first four nonzero terms in the series expansion about x = 0 for a solution to the given equation for x > 0. 19. 9x2y" +9x²y' + 2y = 0 20. 2x(x-1)y" + 3(x-1)y' - y = 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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14. (x²-4)y" + (x + 2)y' + 3y = 0,
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15. 0³y" +0(sin)y' - (tan) y = 0,
at 0 = 0
16. (x²-1)y" - (x-1)y' - 3y = 0, at x = 1
17. (x-1)²y" + (x² - 1)y' - 12y = 0, at x = 1
18. 4x(sinx)y" - 3y = 0, at x = 0
In Problems 19-24, use the method of Frobenius to find at
least the first four nonzero terms in the series expansion about
x = 0 for a solution to the given equation for x > 0.
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19. 9x²y" +9x²y' + 2y = 0
20. 2x(x-1)y" + 3(x-1)y' - y = 0
21. x²y" + xy' + x²y = 0
22. xy"+y' - 4y = 0
23. x²z" + (x²+x)z! -z = 0
24. 3xy" +(2-x)y' - y = 0
In Problems 25-30, use the method of Frobenius to find a
general formula for the coefficient an in a series expansion
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