Test Bank Docx Chapter.4 | Higher-Order Linear Differential

Elementary Differential Equations, 12e (Boyce)

Chapter 4 Higher-Order Linear Differential Equations

1) On which of these intervals is a solution of the following differential equation sure to exist? Select all that apply.

-8 (y) with superscript ((6)) + 6 (t) with superscript (3) (y) with superscript ((4)) + sin(3t)y = (1/(t) with superscript (2) - 1)

A) (- (1/3), (1/3))

B) (0, ∞)

C) (-∞, 0)

D) (-1, 0)

E) (-∞, -2)

F) (-∞, ∞)

Type: MC Var: 1

2) On which of these intervals is a solution of the following differential equation sure to exist? Select all that apply.

((t - 4)) with superscript (2) y''' + (7/8) (e) with superscript (4t) y'' - square root of (5 - t) ∙ + 2y = 0

A) (4, 5]

B) (0, 4)

C) (0, ∞)

D) (0, 5]

E) (4, ∞)

F) [5, ∞)

Type: MC Var: 1

3) On which of these intervals is a solution of the following differential equation sure to exist? Select all that apply.

-4 square root of (t) ∙ y''' + y'' - (tan t) y = -3

A) (0, ∞)

B) (0, (π/2))

C) (0, π)

D) (- (π/2), (π/2))

E) ((π/4), (3π/4))

F) (2, (3π/2))

Type: MC Var: 1

4) Compute the Wronskian W for the set of functions 2x, -3 (x) with superscript (2) , -2 (x) with superscript (3) .

W = ________

Type: SA Var: 1

5) Consider the fourth-order differential equation (y) with superscript ((4)) - 16y = 0. The general solution of this equation can be y = (C) with subscript (1) (e) with superscript (2t) + (C) with subscript (2) (e) with superscript (-2t) + (C) with subscript (3) sinh(2t) + (C) with subscript (4) cosh(2t), where ... are arbitrary real constants.

Type: TF Var: 1

6) Compute the Wronskian W for the set of functions (e) with superscript (7x) , (e) with superscript (-7x) , (e) with superscript (-14x) .

W = ________

Type: SA Var: 1

7) For which of the following homogeneous differential equations is the general solution given by , where (C) with subscript (1) ... (C) with subscript (3) are arbitrary real constants?

A) y'' - 16 = 0

B) y''' - 16 = 0

C) y''' - 16y = 0

D) y'' - 16y = 0

Type: MC Var: 1

8) For which of the following homogeneous differential equations is the general solution given by , where (C) with subscript (1) ... (C) with subscript (4) are arbitrary real constants?

A) (y) with superscript ((4)) + 18 y'' + 81y = 0

B) (y) with superscript ((4)) - 18 y'' + 81y = 0

C) (y) with superscript ((4)) + 9 y'' + 81y = 0

D) (y) with superscript ((4)) - 81y = 0

E) (y) with superscript ((4)) + 81y = 0

Type: MC Var: 1

9) For which of the following homogeneous differential equations is the general solution given by , where (C) with subscript (1) ... (C) with subscript (4) are arbitrary real constants?

A) (y) with superscript ((4)) - 256 y'' = 0

B) (y) with superscript ((4)) - 16 y'' = 0

C) (y) with superscript ((4)) + 8 y''' + 16 y'' = 0

D) (y) with superscript ((4)) - 8 y''' + 16 y'' = 0

Type: MC Var: 1

10) For which of the following homogeneous differential equations is the general solution given by , where (C) with subscript (1) ... (C) with subscript (4) are arbitrary real constants?

A) y''' + -24 y'' - 176 + -384y = 0

B) y''' - -24 y'' + 176 - -384y = 0

C) (y) with superscript ((4)) + -24 y''' - 176 y'' + -384 = 0

D) (y) with superscript ((4)) - -24 y''' + 176 y'' - -384 = 0

Type: MC Var: 1

11) What is the least order of a homogeneous differential equation with constant coefficients for which y = -12 (e) with superscript (8x) + 3.2 sin ((π/2)x) + square root of (3) x is a solution?

Type: SA Var: 1

12) What is the least order of a homogeneous differential equation with constant coefficients for which y = ((6x - 1)) with superscript (5) (e) with superscript (4x) sin(8πx) is a solution?

Type: SA Var: 1

13) What is the least order of a homogeneous differential equation with constant coefficients for which y = (4 - 4(x) with superscript (4)) with superscript (2) (10(e) with superscript (-4.5x) + (3) to the (3) root(e) with superscript (2.5x) - (1/2)(e) with superscript ((3π/2)x)) is a solution?

Type: SA Var: 1

14) What is the least order of a homogeneous differential equation with constant coefficients for which y = 3.2 (x) with superscript (5) + (x) with superscript (6) (e) with superscript (-3.5x) is a solution?

Type: SA Var: 1

15) What is the least order of a homogeneous differential equation with constant coefficients for which y = 7 (x) with superscript (4) + (x) with superscript (6) ( (e) with superscript (-5.5x) + (e) with superscript (5x) ) is a solution?

Type: SA Var: 1

16) What is the least order of a homogeneous differential equation with constant coefficients for which y = 7 (x) with superscript (4) (sin( square root of (6) x) + cos( square root of (7) x)) is a solution?

Type: SA Var: 1

17) What is the least order of a homogeneous differential equation with constant coefficients for which y = -30 (e) with superscript (- square root of (10)x) sin ((7/8)x) + 4cos + (4) to the (3) root (e) with superscript (7x) is a solution?

Type: SA Var: 1

18) What is the least order of a homogeneous differential equation with constant coefficients for which y = square root of ((1/10)) π + 3 (e) with superscript (1.2x) - 2.2cos(5x) + 4.5sin(5.5x) is a solution?

Type: SA Var: 1

19) For which of the following homogeneous differential equations is the general solution given by , where (C) with subscript (1) ... (C) with subscript (4) are arbitrary real constants?

A) (y) with superscript ((4)) - 81y = 0

B) (y) with superscript ((4)) + 81y = 0

C) (y) with superscript ((4)) - 81 = 0

D) (y) with superscript ((4)) + 81 = 0

Type: MC Var: 1

20) What is the general solution of the third-order homogeneous differential equation y''' + 12y'' + 48y' + 64y = 0 ?

A) y = (C) with subscript (1) (e) with superscript (--4t) + (C) with subscript (2) t + (C) with subscript (3) (t) with superscript (2) + (C) with subscript (4)

B) y = (C) with subscript (1) (e) with superscript (-4t) + (C) with subscript (2) t + (C) with subscript (3) (t) with superscript (2) + (C) with subscript (4)

C) y = (C) with subscript (1) (e) with superscript (--4t) + (C) with subscript (2) t + (C) with subscript (3) (t) with superscript (2)

D) y = (C) with subscript (1) (e) with superscript (-4t) + (C) with subscript (2) t + (C) with subscript (3) (t) with superscript (2)

E) y = (C) with subscript (1) (e) with superscript (-4t) + (C) with subscript (2) t + (C) with subscript (3) (e) with superscript (--4t)

Type: MC Var: 1

21) What is the general solution of the third-order homogeneous differential equation y''' - 4y'' + 8y' = 0 ?

A) y = (C) with subscript (1) + (C) with subscript (2) (e) with superscript (2t) cos(4t) + (C) with subscript (3) sin(4t)

B) y = (C) with subscript (1) + (C) with subscript (2) (e) with superscript (2t) cos(2t) + (C) with subscript (3) sin(2t)

C) y = (C) with subscript (1) + (C) with subscript (2) (e) with superscript (-2t) cos(2t) + (C) with subscript (3) sin(2t)

D) y = (C) with subscript (1) + (C) with subscript (2) (e) with superscript (4t) cos(2t) + (C) with subscript (3) sin(2t)

E) y = (C) with subscript (1) + (C) with subscript (2) (e) with superscript (-4t) cos(2t) + (C) with subscript (3) sin(2t)

Type: MC Var: 1

22) What is the general solution of the fifth-order homogeneous differential equation (y) with superscript ((5)) - 6(y) with superscript ((4)) + 9(y) with superscript ((3)) = 0 ?

A) y = (C) with subscript (1) + (C) with subscript (2) t + (C) with subscript (3) (t) with superscript (2) + (C) with subscript (4) (e) with superscript (3t) + (C) with subscript (5) t

B) y = (C) with subscript (1) + (C) with subscript (2) t + (C) with subscript (3) (t) with superscript (2) + (C) with subscript (4) (e) with superscript (-3t) + (C) with subscript (5) t

C) y = (C) with subscript (1) + (C) with subscript (2) t + (C) with subscript (3) (e) with superscript (3t) + (C) with subscript (4) t + (C) with subscript (5) (t) with superscript (2)

D) y = (C) with subscript (1) + (C) with subscript (2) t + (C) with subscript (3) (e) with superscript (-3t) + (C) with subscript (4) t + (C) with subscript (5) (t) with superscript (2)

Type: MC Var: 1

23) What is the general solution of the third-order homogeneous differential equation y''' - 4y'' - 4y' = 0 ?

A) y = (C) with subscript (1) + (C) with subscript (2) (e) with superscript (2t) cos ((square root of (32)/2)t) + (C) with subscript (3) cos

B) y = (C) with subscript (1) + (C) with subscript (2) (e) with superscript (- 2t) cos ((square root of (32)/2)t) + (C) with subscript (3) cos

C) y = (C) with subscript (1) + (C) with subscript (2) (e) with superscript ((4 - square root of (32)/2)t) + (C) with subscript (3) (e) with superscript ((4 + square root of (32)/2)t)

D) y = (C) with subscript (1) + (C) with subscript (2) (e) with superscript ((-4 - square root of (32)/2)t) + (C) with subscript (3) (e) with superscript ((-4 + square root of (32)/2)t)

Type: MC Var: 1

24) The differential equation EI (y) with superscript ((4)) - ky = 0, where E, I, and k are positive constants, arises when modeling vibrating beams. What is the general solution of this equation?

A) y = (C) with subscript (1) (e) with superscript (square root of ((k/EI))t) + (C) with subscript (2) (e) with superscript (- square root of ((k/EI))t) + (C) with subscript (3) t + (C) with subscript (4) t

B) y = (C) with subscript (1) (e) with superscript (((k/EI)) to the (4) roott) + (C) with subscript (2) (e) with superscript (- ((k/EI)) to the (4) roott) + (C) with subscript (3) t + (C) with subscript (4) t

C) y = (C) with subscript (1) (e) with superscript (square root of ((k/EI))t) + (C) with subscript (2) (e) with superscript (- square root of ((k/EI))t) + (C) with subscript (3) cos + (C) with subscript (4) sin

D) y = (C) with subscript (1) (e) with superscript (((k/EI)) to the (4) roott) + (C) with subscript (2) (e) with superscript (- ((k/EI)) to the (4) roott) + (C) with subscript (3) cos + (C) with subscript (4) sin

Type: MC Var: 1

25) Suppose a fourth-order homogeneous linear differential equation with constant coefficients has these characteristic roots: -8.8, 8.8, 10i, -10i

Which of the following terms are part of the general solution of this equation? Here, C denotes an arbitrary real constant.

Select all that apply.

A) C

B) C (e) with superscript (-8.8t)

C) Ct (e) with superscript (-8.8t)

D) C (e) with superscript (-8.8t) sin(10t)

E) cos(10t) + C

F) C sin(10t)

Type: MC Var: 1

26) Suppose a seventh-order homogeneous linear differential equation with constant coefficients has these characteristic roots: 0, 0, 0, 3 - square root of (3) i, 3 + i, - i, i

Which of the following terms are part of the general solution of this equation? Here, C denotes an arbitrary real constant.

Select all that apply.

A) Ct

B) C (t) with superscript (3)

C) (t) with superscript (2) + C

D) C (e) with superscript (3t) cos( square root of (3) t)

E) C (e) with superscript (3t)

F) C (e) with superscript (square root of (3)t) sin(3t)

G) t (e) with superscript (square root of (3)t) + C

H) C sin( square root of (3) t)

Type: MC Var: 1

27) Suppose a ninth-order homogeneous linear differential equation with constant coefficients has these characteristic roots: -6i, -6i, 6i, 6i, square root of (11) , - , - , - , -6.2

Which of the following terms are part of the general solution of this equation? Here, C denotes an arbitrary real constant.

Select all that apply.

A) Ct sin(6t)

B) Ct

C) C

D) C (t) with superscript (square root of (11))

E) C (t) with superscript (2) (e) with superscript (- square root of (11)t)

F) C (e) with superscript (square root of (11)t) cos(6t)

G) C (t) with superscript (2) cos(6t)

H) C (e) with superscript (- square root of (11)t)

Type: MC Var: 1

28) What is the general solution of the third-order linear homogeneous differential equation y''' + 27y = 0 ?

Type: SA Var: 1

29) What is the general solution of the third-order linear homogeneous differential equation y''' + 27y' = 0 ?

Type: SA Var: 1

30) What is the general solution of the third-order linear homogeneous differential equation y''' + 2y'' - 25y' - 50y = 0 ?

Type: SA Var: 1

31) What is the general solution of the fourth-order linear homogeneous differential equation (y) with superscript ((4)) + 8y'' + 16y = 0 ?

Type: SA Var: 1

32) Solve the following initial value problem:

(y) with superscript ((4)) + 9 y'' = 0, y(0) = 0, (0) = 0, y'' (0) = -8, y''' (0) = 27

Type: SA Var: 1

33) Solve the following initial value problem:

y''' - 6 y'' - 9 + 54y = 0, y(0) = 12, (0) = 0, y'' (0) = 0

Type: SA Var: 1

34) Solve the following initial value problem:

y''' + 10 y'' + 25 = 0, y(0) = 6, (0) = 15, y'' (0) = 25

Type: SA Var: 1

35) What is the form of a particular solution of the following nonhomogeneous differential equation?

y''' + 512y = 6 (e) with superscript (9t) + 4 (e) with superscript (64t)

All capital letters in the choices represent arbitrary real constants.

A) A (e) with superscript (9t) + B (e) with superscript (64t)

B) (At + B) (e) with superscript (9t) + (Ct + D) (e) with superscript (64t)

C) A( (e) with superscript (9t) + (e) with superscript (64t) )

D) At( (e) with superscript (9t) + (e) with superscript (64t) )

Type: MC Var: 1

36) What is the form of a particular solution of the following nonhomogeneous differential equation?

(y) with superscript ((4)) + 18 y'' + 81y = 8t (e) with superscript (3t)

All capital letters in the choices represent arbitrary real constants.

A) (A (t) with superscript (3) + B (t) with superscript (2) + Ct + D) (e) with superscript (3t)

B) (A (t) with superscript (2) + Bt + C) (e) with superscript (3t)

C) (At + B) (e) with superscript (3t)

D) At (e) with superscript (3t) + B

Type: MC Var: 1

37) What is the form of a particular solution of the following nonhomogeneous differential equation?

(y) with superscript ((4)) - 10 y''' + 25 y'' = (1/5) (e) with superscript (5t) + square root of (17)

All capital letters in the choices represent arbitrary real constants.

A) A + B (e) with superscript (5t)

B) A (t) with superscript (2) + Bt + C + (D + Et + F) (e) with superscript (5t)

C) (A (t) with superscript (2) + Bt + C)(1 + (e) with superscript (5t) )

D) At + B (t) with superscript (2) (e) with superscript (5t)

Type: MC Var: 1

38) What is the form of a particular solution of the following nonhomogeneous differential equation?

y''' - 30 y'' + 275 - 750y = (6π/7) sin(5t) + (5/4) (e) with superscript (10t)

All capital letters in the choices represent arbitrary real constants.

A) (At + B) (e) with superscript (5t) + (Ct + D) (e) with superscript (10t)

B) A (e) with superscript (5t) sin(5t) + Bcos(5t) + C (e) with superscript (10t)

C) (e) with superscript (5t) (A sin(5t) + B cos(5t)) + C (e) with superscript (10t) + Dt

D) A sin(5t) + B cos(5t) + (Ct + D) (e) with superscript (10t)

Type: MC Var: 1

39) What is the form of a particular solution of the following nonhomogeneous differential equation?

(y) with superscript ((4)) + 16y = -16t (e) with superscript (2t) sin(2t)

All capital letters in the choices represent arbitrary real constants.

A) (A (t) with superscript (2) + Bt + C) (e) with superscript (2t) sin(2t)

B) (A (t) with superscript (2) + Bt + C) (e) with superscript (2t) (sin(2t) + cos(2t))

C) (e) with superscript (2t) ((At + B)sin(2t) + (Ct + D)cos(2t))

D) (e) with superscript (2t) ((A (t) with superscript (2) + Bt + C)sin(2t) + (D + Et + F)cos(2t))

E) (At + B) (e) with superscript (2t) (sin(2t) + cos(2t))

F) (At + B) (e) with superscript (2t) sin(2t)

Type: MC Var: 1

40) What is the form of a particular solution of the following nonhomogeneous differential equation?

(y) with superscript ((4)) + 8 y'' + 16y = square root of ((1/13)) cos(2t) + (13/10) t

All capital letters in the choices represent arbitrary real constants.

A) A cos(2t) + B sin(2t) + Ct + D

B) (A (t) with superscript (2) + Bt + C)cos(2t) + (D + Et + F)sin(2t) + Gt + H

C) A (t) with superscript (2) cos(2t) + Bt + C

D) (At + B)cos(2t) + (Ct + D)sin(2t) + Et

E) (At + B)cos(2t) + (Ct + D)sin(2t) + Et + F

Type: MC Var: 1

41) What is the form of a particular solution of the following nonhomogeneous differential equation?

y''' - 12 y'' + 48 - 64y = (4) to the (3) root ( (e) with superscript (-4t) + (e) with superscript (4t) )

All capital letters in the choices represent arbitrary real constants.

A) A (e) with superscript (-4t) + B (e) with superscript (4t)

B) (A (t) with superscript (2) + Bt + C)( (e) with superscript (-4t) + (e) with superscript (4t) )

C) (A (t) with superscript (2) + Bt + C) (e) with superscript (-4t) + (D + Et + F) (e) with superscript (4t)

D) A (e) with superscript (4t) + (B (t) with superscript (3) + C (t) with superscript (2) + Dt + E) (e) with superscript (-4t)

E) A (e) with superscript (-4t) + (B (t) with superscript (3) + C (t) with superscript (2) + Dt + E) (e) with superscript (4t)

Type: MC Var: 1

42) What is the form of a particular solution of the following nonhomogeneous differential equation?

y''' - 4 y'' + 8 = (5/3) (e) with superscript (2t) sin(2t)

All capital letters in the choices represent arbitrary real constants.

A) (At + B) (e) with superscript (2t) sin(2t)

B) A (e) with superscript (2t) sin(2t) + Bcos(2t)

C) A (e) with superscript (2t) sin(2t)

D) (At + B) (e) with superscript (2t) sin(2t) + (Ct + D)cos(2t)

E) (At + B) (e) with superscript (2t) (sin(2t) + cos(2t))

Type: MC Var: 1

43) What is the form of a particular solution of the following nonhomogeneous differential equation?

(y) with superscript ((5)) - 10 (y) with superscript ((4)) + 25 (y) with superscript ((3)) = 13t (e) with superscript (-5t)

All capital letters in the choices represent arbitrary real constants.

A) A (e) with superscript (-5t)

B) (At + B) (e) with superscript (-5t)

C) (A (t) with superscript (2) + Bt + C) (e) with superscript (-5t)

D) (A (t) with superscript (3) + B (t) with superscript (2) + Ct + D) (e) with superscript (-5t)

Type: MC Var: 1

44) What is the form of a particular solution of the following nonhomogeneous differential equation?

(y) with superscript ((4)) + 8 y'' + 16y = (π/2) cos(2t) + (e) with superscript (2t)

Use capital letters A, B, C, ... to represent arbitrary real constants. Do not actually solve for the constants.

Type: SA Var: 1

45) What is the form of a particular solution of the following nonhomogeneous differential equation?

(y) with superscript ((5)) - 36 y''' = (e) with superscript (6t) + 15 (t) with superscript (2) + 16

Use capital letters A, B, C, ... to represent arbitrary real constants. Do not actually solve for the constants.

Type: SA Var: 1

46) Consider the nonhomogeneous differential equation y''' - = 4 (e) with superscript (3t) + 4 (e) with superscript (-3t) . The functions (y) with subscript (1) = 1 , (y) with subscript (2) = (e) with superscript (t) , and (y) with subscript (3) = (e) with superscript (-t) form a fundamental set of solutions of the corresponding homogeneous equation y''' - = 0.

Compute the Wronskian, W(t), for { (y) with subscript (1) , (y) with subscript (2) , (y) with subscript (3) }

Type: SA Var: 1

47) Consider the nonhomogeneous differential equation y''' - = 9 (e) with superscript (7t) + 10 (e) with superscript (8t) . The functions (y) with subscript (1) = 1 , (y) with subscript (2) = (e) with superscript (t) , and (y) with subscript (3) = (e) with superscript (-t) form a fundamental set of solutions of the corresponding homogeneous equation y''' - = 0.

Suppose the method of variation of parameters is to be used to find a particular solution (y) with subscript (p) of the nonhomogeneous differential equation. Then, = (u) with subscript (1) (y) with subscript (1) + (u) with subscript (2) (y) with subscript (2) + (u) with subscript (3) (y) with subscript (3) , for appropriately-chosen functions , , and . As part of the process of forming this solution, find the following quantities.

(a) (W) with subscript (1) (t) = ________, (W) with subscript (2) (t) = ________, (W) with subscript (3) (t) = ________

(b) (u') with subscript (1) (t) = ________, (u') with subscript (2) (t) = ________, (u') with subscript (3) (t) = ________

(b) (u') with subscript (1) (t) = -(9 (e) with superscript (7t) + 10 (e) with superscript (8t) ), (u') with subscript (2) (t) = (9(e) with superscript (6t) + 10(e) with superscript (7t)/2) , (u') with subscript (3) (t) = (9(e) with superscript (8t) + 10(e) with superscript (9t)/2)

(c) (u) with subscript (1) (t) = - (9/7) (e) with superscript (7t) - (5/4) (e) with superscript (8t) , (u) with subscript (2) (t) = (3/4) (e) with superscript (6t) + (5/7) , (u) with subscript (3) (t) = (9/16) + (5/9) (e) with superscript (9t)

Type: ES Var: 1

48) Consider the following third-order nonhomogeneous differential equation:

y''' + 36 = 3tan(6t), 0 < t < (π/12)

Find three functions (y) with subscript (1) , , and that form a fundamental set and are such that the general solution of the corresponding homogeneous equation y''' + 36 = 0 is given by , where (C) with subscript (1) , (C) with subscript (2) , and (C) with subscript (3) are arbitrary real constants.

(y) with subscript (1) = ________, (y) with subscript (2) = ________, (y) with subscript (3) = ________

Type: ES Var: 1

49) Consider the following third-order nonhomogeneous differential equation:

y''' + 36 = -6.5tan(6t), 0 < t < (π/12)

Compute the Wronskian, W(t), for the set of functions (y) with subscript (1) , (y) with subscript (2) , and (y) with subscript (3) that form a fundamental set and are such that the general solution of the corresponding homogeneous equation y''' + 36 = 0 is given by , where (C) with subscript (1) , (C) with subscript (2) , and (C) with subscript (3) are arbitrary real constants.

Type: SA Var: 1

50) Consider the following third-order nonhomogeneous differential equation:

y''' + 25 = 7tan(5t), 0 < t < (π/10)

(a) (u') with subscript (1) (t) = ________, (u') with subscript (2) (t) = ________, (u') with subscript (3) (t) = ________

(b) (u) with subscript (1) (t) = ________, (u) with subscript (2) (t) = ________, (u) with subscript (3) (t) = ________

(u') with subscript (2) (t) = - (7/25) sin(5t)

(u') with subscript (3) (t) = - (7/25) ((sin) with superscript (2)(5t)/cos(5t))

(b) (u) with subscript (1) (t) = (7/125) ln|sec(5t)|

(u) with subscript (2) (t) = (7/125) cos(5t)

(u) with subscript (3) (t) = (7/125) (sin(5t) - ln|sec(5t) + tan(5t)|)

Type: ES Var: 1

51) Use the method of variation of parameters to solve the following third-order nonhomogeneous differential equation:

y''' - 3 y'' + 3 - y = square root of (t) (e) with superscript (t)

A) y = (C) with subscript (1) (e) with superscript (t) + (C) with subscript (2) t + (C) with subscript (3) (t) with superscript (2) - (2/5) (t) with superscript ((5/2))

B) y = (C) with subscript (1) (e) with superscript (t) + (C) with subscript (2) t + (C) with subscript (3) (t) with superscript (2) + (8/105) (t) with superscript ((7/2))

C) y = (C) with subscript (1) (e) with superscript (t) + (C) with subscript (2) t + (C) with subscript (3) (t) with superscript (2) + ((1/7)(t) with superscript ((7/2)) - (2/5)(t) with superscript ((7/2)))

D) y = (C) with subscript (1) (e) with superscript (-t) + (C) with subscript (2) t + (C) with subscript (3) (t) with superscript (2) + (8/105) (t) with superscript ((7/2)) (e) with superscript (t)

E) y = (C) with subscript (1) (e) with superscript (-t) + (C) with subscript (2) t + (C) with subscript (3) (t) with superscript (2) + ((1/7)(t) with superscript ((7/2)) - (2/5)(t) with superscript ((7/2))) (e) with superscript (t)

F) y = (C) with subscript (1) (e) with superscript (-t) + (C) with subscript (2) t + (C) with subscript (3) (t) with superscript (2) - (2/5) (t) with superscript ((5/2)) (e) with superscript (t)

Type: MC Var: 1

52) Compute the Wronskian W for the set of functions (e) with superscript (2x) , x, (x) with superscript (2) .

Type: SA Var: 1

53) What is the general solution of the third-order homogeneous Cauchy Euler differential equation (x) with superscript (3)y''' + xy' - y = 0 ?

A) y = (C) with subscript (1) x + (C) with subscript (2) x ln x + (C) with subscript (3) (x) with superscript (2) ln x

B) y = (C) with subscript (1) x + (C) with subscript (2) x ln x + (C) with subscript (3) x ((ln x)) with superscript (2)

C) y = (C) with subscript (1) (x) with superscript (-1) + (C) with subscript (2) ln x + (C) with subscript (3) ((ln x)) with superscript (2)

D) y = (C) with subscript (1) (x) with superscript (-1) + (C) with subscript (2) ln() + (C) with subscript (3) ((ln((x) with superscript (-1)))) with superscript (2)

Type: MC Var: 1

54) What is the general solution of the third-order homogeneous Cauchy Euler differential equation $(x) with superscript (3)y''' + (x) with superscript (2)y'' - 2xy' + 2y = 0$ ?

A) y = (C) with subscript (1) ln x + (C) with subscript (2) ln( (x) with superscript (-1) ) + (C) with subscript (3) ln( (x) with superscript (2) )

B) y = (C) with subscript (1) (x) with superscript (-2) + (C) with subscript (2) (x) with superscript (-1) + (C) with subscript (3) x

C) y = (C) with subscript (1) (x) with superscript (2) + (C) with subscript (2) x + (C) with subscript (3) (x) with superscript (-1)

D) y = (C) with subscript (1) ln x + (C) with subscript (2) ((ln x)) with superscript (2) + (C) with subscript (3) ((ln x)) with superscript (-1)

Type: MC Var: 1

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Chapter 4 Higher-Order Linear Differential Equations

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