Books
in black and white
Main menu
Share a book About us Home
Books
Biology Business Chemistry Computers Culture Economics Fiction Games Guide History Management Mathematical Medicine Mental Fitnes Physics Psychology Scince Sport Technics
Ads

Elementary Differential Equations and Boundary Value Problems - Boyce W.E.

Boyce W.E. Elementary Differential Equations and Boundary Value Problems - John Wiley & Sons, 2001. - 1310 p.
Download (direct link): elementarydifferentialequations2001.pdf
Previous << 1 .. 132 133 134 135 136 137 < 138 > 139 140 141 142 143 144 .. 609 >> Next

PROBLEMS In each of Problems 1 through 14 solve the given differential equation by means of a power series about the given point x0. Find the recurrence relation; also find the first four terms in each of two linearly independent solutions (unless the series terminates sooner). If possible, find the general term in each solution.
1. y" 1 2. y" - xyf - 0
y II
II
,0 x
x 0,
II
II y
0
3. y" 0 1 4. y" + k2 x 2y I 0, x0 I 0, k a constant
x
"

y
1
x

5. (1 - x)y" + y = 0, x0 I0 6. (2 + x 2)y" - xy + 4y = 0, x0 = 0
7. y " + xy' + 2y = 0, x00 I0 8. xy "+ y' + II

x
0,
II
y
x
9. (1 + x2)y" - 4xy' + 6y : I 0, x0 I 0 10. (4 2) +
x 2
1 y
II
0,
x

I
0
11. (3 - x2)y" - 3xy; - y = 0, x0 0I 0 12. (1 - x)y" + xy' - y = 0, x00 = 0
13. 2y " + xy' + 3y = 0, x 0 I 0 0 14. 2y + 2
x II
+ 0
0x
0,
II
y
3
+
248
Chapter 5. Series Solutions of Second Order Linear Equations
In each of Problems 15 through 18:
(a) Find the first five nonzero terms in the solution of the given initial value problem.
(b) Plot the four-term and the five-term approximations to the solution on the same axes.
(c) From the plot in part (b) estimate the interval in which the four-term approximation is reasonably accurate.
> 15. y" xy y = 0, y(0) = 2, y (0) = 1; see Problem 2
> 16. (2 + x2)y" xy' + 4y = 0, y(0) = 1, y'(0) = 3; see Problem 6
> 17. y" + xy' + 2y = 0, y(0) = 4, y'(0) = 1; see Problem 7
> 18. (1 x)y" + xy1 y = 0, y(0) = 3, y'(0) = 2; see Problem 12
19. By making the change of variable x 1 = t and assuming that y is a power series in t, find two linearly independent series solutions of
Previous << 1 .. 132 133 134 135 136 137 < 138 > 139 140 141 142 143 144 .. 609 >> Next