2 B D Page view A0. Determine whether a member of the famTly can befound that satisfies the boundary conditions.33. y13. y = cje cos x+ cze sin x; y-2y +2y = 0(a) y(0) = 1, y'(7) = 0 (b) y(0) = 1, y(7) = -134. 2(c) y(0) = 1, y= 1 (d) y(0) = 0, y(7) = 0.14. y = c + czr + 3: xy-5xy + 8y 24(a) y(-1) = 0, y(1) = 4 (b) y(0) = 1, y(1) = 2(c) y(0) = 3, y(1) = 035. (a(d) y(1) = 3, y(2) = 154.1.2 HOMOGENEOUS EQUATIONS(bIn Problems 5-22 determine whether the given set of func-tions is linearly independent on the interval (,).15. fi(x) = x, f2(x) = x², f;(x) = 4x – 3x36. (aT6. -0. ) = x, (x) =e17. fi(x) = 5, f(x) = cos*x, fi(x) = sin'x(b)18. fi(x) = cos 2.x, f:(x) = 1, fa(x) = cos-x19. fi(x) = x, fx) = x – 1, fAx) = x+ 3(c)20. fi(x) = 2 + x, fa(x) = 2 +x|(d)130CHAPTER 4HIGHER-ORDER DIFFERENTIAL EQUATIONS

To check linear dependent or linear independent by using result: "the set S is linearly dependent…

4.1.2 HOMOGENEOUS EQUATIONS In Problems 15-22 determine whether the given set of func- tions is linearly independent on the interval (-0, oc). 15. fi(x) = x, f2(x) = x, fs(x) = 4x - 3x2 36. (a %3D 16. i 0, JX) = x, f3(x) = e 17. fi(x) = 5, f2(x) = cos x, f(x) = sinx |3D %3D (b 18. fi(x) = cos 2.x, f2(x) = 1, fa(x) = cos-r %3D 10

4.1.2 HOMOGENEOUS EQUATIONS In Problems 15-22 determine whether the given set of func- tions is linearly independent on the interval (-0, oc). 15. fi(x) = x, f2(x) = x, fs(x) = 4x - 3x2 36. (a %3D 16. i 0, JX) = x, f3(x) = e 17. fi(x) = 5, f2(x) = cos x, f(x) = sinx |3D %3D (b 18. fi(x) = cos 2.x, f2(x) = 1, fa(x) = cos-r %3D 10

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

2 B D Page view A
0. Determine whether a member of the famTly can be
found that satisfies the boundary conditions.
33. y
13. y = cje cos x+ cze sin x; y-2y +2y = 0
(a) y(0) = 1, y'(7) = 0 (b) y(0) = 1, y(7) = -1
34. 2
(c) y(0) = 1, y
= 1 (d) y(0) = 0, y(7) = 0.
14. y = c + czr + 3: xy-5xy + 8y 24
(a) y(-1) = 0, y(1) = 4 (b) y(0) = 1, y(1) = 2
(c) y(0) = 3, y(1) = 0
35. (a
(d) y(1) = 3, y(2) = 15
4.1.2 HOMOGENEOUS EQUATIONS
(b
In Problems 5-22 determine whether the given set of func-
tions is linearly independent on the interval (,).
15. fi(x) = x, f2(x) = x², f;(x) = 4x – 3x
36. (a
T6. -0. ) = x, (x) =e
17. fi(x) = 5, f(x) = cos*x, fi(x) = sin'x
(b)
18. fi(x) = cos 2.x, f:(x) = 1, fa(x) = cos-x
19. fi(x) = x, fx) = x – 1, fAx) = x+ 3
(c)
20. fi(x) = 2 + x, fa(x) = 2 +x|
(d)
130
CHAPTER 4
HIGHER-ORDER DIFFERENTIAL EQUATIONS

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