EMCF-9-F14
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Transcript of EMCF-9-F14
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8/9/2019 EMCF-9-F14
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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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