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MATH 3321 Final Exam | Questions and Answers Latest Update 2026/2027
(Graded A+) - University of Houston
Final
You scored 100 out of 130
Question 1
Your answer is INCORRECT.
Give the differential equation that has y4 = Cx 2 + 3 x as a general solution.
2 y4 − 9 x
a) y′=
4 xy3
′ 2 y4 − 3 x
b) y =
4 xy3
2 y4 − 6 x + 3
c) y′=
4 y3
′ 2 y3 − 3
d) y =
4 xy3
2 y4 − 6 x
e) y′=
4 xy3
f) None of the above.
Question 2
Your answer is CORRECT.
Find the general solution of x2 y′ + x y = 4x cos(4x) .
1 −1 −1
a) y= x sin(4x) + Cx
4
b) y = −x−1 sin(4x) + Cx−1
c) y = −4x−1 sin(4x) + Cx−1
d) y = x sin(4x) + Cx
e) y = x−1 sin(4x) + Cx−1
1/9
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f) None of the above.
Question 3
Your answer is CORRECT.
The differential equation for the family of curves y3 = Cx 4 + 4 is
3
4y − 16
y′ = .
3xy2
Find the family of orthogonal trajectories.
32
a) 3x2 + 4y2 − =C
y
b) 3x2 + 4y2 + 32 ln(y) = C
c) 3x2 + 4y2 − 32 ln(y) = C
64
d) 3x2 + 4y2 − =C
y
32
e) 3x2 + 4y2 + =C
y
f) None of the above.
Question 4
Your answer is CORRECT.
′′
Give the general solution to y − 2y ′ + 10y = 0
a) C1ex cos(3 x) + C2ex sin(3 x)
b) C1 e−x + C2 e−3 x
c) C1e−x cos(3 x) + C2e−x sin(3 x)
d) C1ex + C2xex
e) C1 ex + C2 e3 x
f) None of the above.
2/9
MATH 3321 Final Exam | Questions and Answers Latest Update 2026/2027
(Graded A+) - University of Houston
Final
You scored 100 out of 130
Question 1
Your answer is INCORRECT.
Give the differential equation that has y4 = Cx 2 + 3 x as a general solution.
2 y4 − 9 x
a) y′=
4 xy3
′ 2 y4 − 3 x
b) y =
4 xy3
2 y4 − 6 x + 3
c) y′=
4 y3
′ 2 y3 − 3
d) y =
4 xy3
2 y4 − 6 x
e) y′=
4 xy3
f) None of the above.
Question 2
Your answer is CORRECT.
Find the general solution of x2 y′ + x y = 4x cos(4x) .
1 −1 −1
a) y= x sin(4x) + Cx
4
b) y = −x−1 sin(4x) + Cx−1
c) y = −4x−1 sin(4x) + Cx−1
d) y = x sin(4x) + Cx
e) y = x−1 sin(4x) + Cx−1
1/9
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f) None of the above.
Question 3
Your answer is CORRECT.
The differential equation for the family of curves y3 = Cx 4 + 4 is
3
4y − 16
y′ = .
3xy2
Find the family of orthogonal trajectories.
32
a) 3x2 + 4y2 − =C
y
b) 3x2 + 4y2 + 32 ln(y) = C
c) 3x2 + 4y2 − 32 ln(y) = C
64
d) 3x2 + 4y2 − =C
y
32
e) 3x2 + 4y2 + =C
y
f) None of the above.
Question 4
Your answer is CORRECT.
′′
Give the general solution to y − 2y ′ + 10y = 0
a) C1ex cos(3 x) + C2ex sin(3 x)
b) C1 e−x + C2 e−3 x
c) C1e−x cos(3 x) + C2e−x sin(3 x)
d) C1ex + C2xex
e) C1 ex + C2 e3 x
f) None of the above.
2/9
