Page 306 - Schaum's Outline of Differential Equations

CHAP. 28] SERIES SOLUTIONS NEAR A REGULAR SINGULAR POINT 289

Supplementary Problems

In Problems 28.25 through 28.33, find two linearly independent solutions to the given differential equations.

2
2
28.25. 2x y"-xy' + (l-x)y = 0 28. 26. 2x y" + (x 2 - x)y' + y = 0
2
2
28.27. 3x y" - 2xy' - (2 + x )y = 0 28.28. xy" + y'-y = 0
2
2
2
3
28.29. x y" + xy' + x y = 0 28. 30. x y" + (x-x )y'-y = 0
2
2
28.31. xy" -(x + l)y'-y = 0 28.32. 4x y" + (4x + 2x )y' + (3x - l)y = 0
2
2
28.33. x y" + (x - 3x)y' -(x-4)y = 0
In Problem 28.34 through 28.38, find the general solution to the given equations using the method described in Problem 28.22.
2
2
28.34. 4x y" + 4xy' - y = 0 28.35. x y"-3xy' + 4y = 0
2
2
28. 36. 2x y" + 1 Ley' + 4y = 0 28.37. x y"-2y = 0
2
28.38. x y"-6xy' = 0