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MATH 3321 Quiz 9 10/8/14

1. The general solution of y(4) 5y 36y = 0 is:

(a) y = C1cos 3x + C2sin 3x + C3e2x + C4e2x

(b) y = C1cos 3x + C2sin 3x + C3cos 2x + C4sin 2x

(c) y = C1cos 2x + C2sin 2x + C3e3x + C4e3x

(d) y = C1cos 2x + C2sin 2x + C3e3x + C4xe3x

(e) None of the above.

2. The general solution of y(4) y 3y + 17y 30y = 0 is:

(a) y = C1ex cos 2x + C2ex sin 2x + C3e3x + C4e2x

(b) y = C1cos 3x + C2sin 3x + C3e3x + C4e2x

(c) y = C1ex cos 2x + C2ex sin 2x + C3e3x + C4e2x

(d) y = C1cos 2x + C2sin 2x + C3e3x + C4e

2x

(e) None of the above.

3. The general solution of y + 5y + 7y + 3y = 0 is:

(a) y = C1ex + C2xex + C3e3x

(b) y

=C

1ex

+C

2xex

+C

3e3x

(c) y = C1ex + C2xex + C3e3x

(d) y = C1ex + C2xex + C3e3x

(e) None of the above.

4. The general solution of y(4) + 2y + 9y 2y 10y = 0 is:

(a) y = C1ex cos 3x + C2ex sin 3x + C3ex + C4ex

(b) y = C1ex

cos 3x + C2ex

sin 3x + C3ex

+ C4xex

(c) y = C1ex cos 3x + C2ex sin 3x + C3ex + C4xex

(d) y = C1e3x cos x + C2e3x sin x + C3ex + C4ex

(e) None of the above.

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5. The linear, constant coefficient, homogeneous equation of least order that has

y= 2e2x 3e2x + 4 sin 2x + 5

as a solution is:

(a) y(4) 16y = 0

(b) y(5) 16y = 0

(c) y(5) 36y = 0

(d) y(4) + 16y = 0

(e) None of the above.

6. The linear, constant coefficient, homogeneous equation of least order that has

y= 9sin 2x + 4xex 3x

as a solution is:

(a) y(6) 2y(5) + 6y(4) 8y + 4y = 0

(b) y(4) + 2y + 5y + 8y + 4y= 0

(c) y(5) + 2y(4) + 5y + 8y + 4y = 0

(d) y(6) + 2y(5) + 5y(4) + 8y + 4y = 0

(e) None of the above.

7. A particular solution of y 5y + 8y 4y= 4e2x 2ex is:

(a) z= 2xe2x 2ex

(b) z= 2x2e2x 2xex

(c) z= 2xe2x + 2x2ex

(d) z= x2e2x 2xex

(e) None of the above.

8. The general solution of y y 8y + 12y = 2 5e3x + 4e2x is:

(a) y = C1e2x

+ C2xe2x

+ C3e3x

+ 16

15xe

3x

+ 14e

2x

(b) y = C1e2x + C2xe2x + C3e3x + 16

14e3x + 1

8x2e2x

(c) y = C1e2x + C2xe2x + C3e3x 13

15e3x + 14e

2x

(d) y = C1e2x + C2xe2x + C3e3x + 16

15xe3x + 14x

2e2x

(e) None of the above.

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9. A particular solution of y(4) 3y 4y= 2e2x ex + 4 cos x will have the form:

(a) z= Ae2x + Bxex + Ccos x + D sin x

(b) z= Ax2e2x + Bxex + Cx cos x + Dx sin x

(c) z= Axe2x + Bex + Ccos x + D sin x

(d) z= Axe2x

+ Bex

+ Cx cosx + Dx sin x(e) None of the above.

10. A particular solution of y + y + y + y= 2ex ex + 4x will have the form:

(a) z= Aex + Bxex + Cx + D

(b) z= Aex + Bxex + Cx

(c) z= Axex + Bex + Cx + D

(d) z= Aex + Bxex + C

(e) None of the above.

11. The general solution of

y(4) + 4y + 13y + 36y + 36y = 5e2x + sin 2x + 6

will have the form:

(a) y = C1e2x +C2xe2x +C3cos 3x+C4sin 3x+Ae2x +B cos 2x+Csin 2x+Dx +E

(b) y = C1e2x

+ C2xe2x

+ C3cos 3x + C4sin 3x + Ax2e2x

+ B cos 2x + Csin 2x + D(c) y = C1e2x + C2xe2x + C3cos 3x + C4sin 3x + Ae2x + B cos 2x + Csin 2x + D

(d) y = C1e2x + C2xe2x + C3cos 3x + C4sin 3x + Ax2e2x + B cos 2x + Csin 2x + Dx

(e) None of the above.

12. The general solution of y(4) + 5y 36y = 2cos 3x + 3xe2x will have the form:

(a) y = C1cos 2x + C2sin 2x + C3e3x + C4e3x + Ax cos 2x + Bx sin 2x + (Cx + D)e2x

(b) y = C1cos 3x+C2sin 3x+C3e2x

+C4xe2x

+Ax cos 3x+Bx sin 3x+ (Cx3

+Dx2

)e2x

(c) y = C1cos 3x + C2sin 3x +C3e2x + C4e

2x + Ax cos 3x + Bx sin 3x + (Cx2 + Dx)e2x

(d) y = C1cos 3x +C2sin 3x +C3e2x +C4xe

2x +Ax cos 3x+ Bx sin 3x+ (Cx+D)e2x

(e) None of the above.

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