MATH 3321 Final Exam | Questions & Verified Answers | 2026/2027 Updated | University of Houston -PDF

MATH 3321 Final Exam | Questions & Verified Answers | 2026/2027 Updated |
University of Houston -PDF

Final

You scored 120 out of 130
Question 1
Your answer is CORRECT.
Give the differential equation that has y4 = Cx 5 + x as a general solution.


′ 5 y3 − 4
a) y =
4 xy3

5 y4 − 5 x
b) y′=
4 xy3

5 y4 − 5 x + 1
c) y′ =
4 y3
5 y4 − 6 x
d) y′=
4 xy3

5 y4 − 4 x
e) y′=
4 xy3

f) None of the above.


Question 2
Your answer is CORRECT.
Find the general solution of x y′ + 3 y = 4x−2 e−4x .


a) y = 4x−3 e−4x + Cx−3

b) y = −x−3 e−4x + Cx−3
1 −3 −4x −3
c) y= x e + Cx
4
d) y = −x−3 e4x + Cx−3


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, Final

You scored 120 out of 130
Question 1
Your answer is CORRECT.
Give the differential equation that has y4 = Cx 5 + x as a general solution.


′ 5 y3 − 4
a) y =
4 xy3

5 y4 − 5 x
b) y′=
4 xy3

′ 5 y4 − 5 x + 1
c) y =
4 y3
5 y4 − 6 x
d) y′=
4 xy3

5 y4 − 4 x
e) y′=
4 xy3

f) None of the above.


Question 2
Your answer is CORRECT.
Find the general solution of x y′ + 3 y = 4x−2 e−4x .


a) y = 4x−3 e−4x + Cx−3

b) y = −x−3 e−4x + Cx−3
1 −3 −4x −3
c) y= x e + Cx
4
d) y = −x−3 e4x + Cx−3


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, e) y = −x3 e−4x + Cx3

f) None of the above.



Question 3
Your answer is CORRECT.
The differential equation for the family of curves y2 = Cx 3 + 5 is
′ 3y2 − 15
y = .
2xy
Find the family of orthogonal trajectories.


60
a) 2x2 + 3y2 − =C
y
30
b) 2x2 + 3y2 + =C
y

c) 2x2 + 3y2 − 30 ln(y) = C

d) 2x2 + 3y2 + 30 ln(y) = C
30
e) 2x2 + 3y2 − =C
y

f) None of the above.



Question 4
Your answer is CORRECT.
Give the general solution to y ′′ + 4y ′ + 13y = 0


a) C1 e−2 x + C2 xe−2 x

b) C1e2 x cos(3 x) + C2e2 x sin(3 x)
c) C1e−2 x cos(3 x) + C2e−2 x sin(3 x)

d) C1 e−2 x + C2 e3 x

e) C1 e2 x + C2 e−3 x
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