Math mcqs...Correct answer pls
Jim_Ak
hw1.pdf
Online MATH 275 Homework 01 Due : 9/2/2015
Please show all steps and submit scanned copy of your work on Blackboard by 9/2 before 11:59 pm.
1. The order of the differential equation d2y
dx2 + 4x
dy
dx + y cos x =
d3(e2x)
dx3 is:
(a) 1
(b) 2
(c) 3
(d) 4
(e) None of the above.
2. The order of the differential equation ∂2u
∂x2 +
∂3u
∂x2∂y + ∂u
∂y = xyu4 is:
(a) 1
(b) 2
(c) 3
(d) 4
(e) None of the above.
3. The set of all solutions of y′ − 6x = 4e2x is:
(a) y = 3x2 + 2e2x + C
(b) y = 3x2 + 2e2x
(c) y = 3x2 + 2e2x + Cx
(d) y = 2e2x − 3x2 + C (e) None of the above.
4. The set of all solutions of dy
dx = 3y is:
(a) y = e3x
(b) y = Ce−3x
(c) y = e3x + C
(d) y = Ce3x
(e) None of the above.
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5. The set of all solutions of y′′ = 12x2 − 4 cos 2x + 6 is:
(a) y = x4 − cos 2x + 6x + Cx (b) y = x4 + sin 2x + 3x2 + C
(c) y = x4 + cos 2x + 3x2 + C1x + C2
(d) y = x4 − sin 2x + 6x2 + C1x2 + C2x (e) None of the above.
6. The value(s) of λ such that y = eλx is a solution of
y′′ − 5y′ + 6y = 0
are:
(a) λ = 5
(b) λ = 3, λ = 2
(c) λ = −1, λ = 5 (d) λ = −3, λ = −2 (e) None of the above.
7. The value(s) of λ such that y = eλx is a solution of
d2y
dx2 + 8
dy
dx + 16y = 0
are:
(a) λ = 4, λ = −4 (b) λ = 4
(c) λ = −4 (d) λ = −8, λ = −2 (e) None of the above.
8. The differential equation which has y2 = Cx3 − 2 as its general solution is:
(a) y′ = 3y2 + 6
2xy
(b) y′ = y2 + 2
2x
(c) y′′ = 2yy′
3x2
(d) x2y′′ − 2xy′ + 2y = 0 (e) None of the above.
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9. The differential equation which has y = C1e x + C2e
3x as its general solution is:
(a) y′ − 3y = 0 (b) y′′ − 2y′ − 3y = 0 (c) x2y′′ − 3xy′ + 3y = 0 (d) y′′ − 4y′ + 3y = 0 (e) None of the above.
10. The differential equation which has y = C1x + C2x 3 as its general solution is:
(a) y′ − 3x2y = 0 (b) x2y′′ − 3xy′ + 3y = 0 (c) x2y′′ − 4xy′ + 6y = 0 (d) y′′ − 4y′ + 3y = 0 (e) None of the above.
11. The value(s) of r such that y = xr is a solution of
d2y
dx2 −
1
x
dy
dx −
8
x2 y = 0
are
(a) r = −2 (b) r = −4, r = 2 (c) r = 4, r = −2 (d) r = 4
(e) None of the above.
12. The value(s) of r such that y = xr is a solution of
x2y′′ − 3xy′ + 5y = 0
are
(a) r = 5
(b) r = −2, r = 5 (c) r = −5, r = 1 (d) r = −2, r = 2 (e) None of the above.
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