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MATH 3321 Test 1 | Questions and Answers Latest Update 2026/2027
(Graded A+) - University of Houston
Test 1
You scored 70 out of 70
Question 1
Your answer is CORRECT.
Give the differential equation that has y = C1 + C2x−3 + x as its general solution.
a) x y′′ − 2y′ = 4
b) x y′′ − 4y′ = −4
c) x y′′ + 4y′ = 4
d) x y′ + 4y = 4
e) x y′′ + 4y′ = −2
f) None of the above.
Question 2
Your answer is CORRECT.
xy − 2y
Give the general solution of y′ = .
y2 +1
a) y2 + ln(y) = −1/2 x2 + 2 x + C
b) y2 − 4 ln(y) = −2 x2 + 8 x + C
c) y2 + 2 ln(y) = x2 − 4 x + C
d) y2 + 2 ln(y) = x3 − 4 x2 + C
e) y2 + ln(y) = −2 ln(y)x − 2 x + C
f) None of the above.
Question 3
1/5
, Print Test
Your answer is CORRECT.
2
Find the general solution of x 2y ′ = e3x − 3xy .
x
2
a) y= e3x + Cx−3
x3
2
b) y= e3x + Cx−3
3x3
2x3
y= e3x + Cx3
c) 3
3x3
y=− e3x + Cx3
d) 2
e) 2 3x
y= e +C
3x3
f) None of the above.
Question 4
Your answer is CORRECT.
Given the one-parameter family of curves y2 = Cx 3 − 2 . Find the family of orthogonal
trajectories.
a) 2x2 + 3y2 − 12 ln(y) = C
12
b) 2x2 + 3y2 + =C
y
12
c) 2x2 + 3y2 − =C
y
d) 2x2 + 3y2 + 12 ln(y) = C
24
e) 2x2 + 3y2 + =C
y
f) None of the above.
2/5
MATH 3321 Test 1 | Questions and Answers Latest Update 2026/2027
(Graded A+) - University of Houston
Test 1
You scored 70 out of 70
Question 1
Your answer is CORRECT.
Give the differential equation that has y = C1 + C2x−3 + x as its general solution.
a) x y′′ − 2y′ = 4
b) x y′′ − 4y′ = −4
c) x y′′ + 4y′ = 4
d) x y′ + 4y = 4
e) x y′′ + 4y′ = −2
f) None of the above.
Question 2
Your answer is CORRECT.
xy − 2y
Give the general solution of y′ = .
y2 +1
a) y2 + ln(y) = −1/2 x2 + 2 x + C
b) y2 − 4 ln(y) = −2 x2 + 8 x + C
c) y2 + 2 ln(y) = x2 − 4 x + C
d) y2 + 2 ln(y) = x3 − 4 x2 + C
e) y2 + ln(y) = −2 ln(y)x − 2 x + C
f) None of the above.
Question 3
1/5
, Print Test
Your answer is CORRECT.
2
Find the general solution of x 2y ′ = e3x − 3xy .
x
2
a) y= e3x + Cx−3
x3
2
b) y= e3x + Cx−3
3x3
2x3
y= e3x + Cx3
c) 3
3x3
y=− e3x + Cx3
d) 2
e) 2 3x
y= e +C
3x3
f) None of the above.
Question 4
Your answer is CORRECT.
Given the one-parameter family of curves y2 = Cx 3 − 2 . Find the family of orthogonal
trajectories.
a) 2x2 + 3y2 − 12 ln(y) = C
12
b) 2x2 + 3y2 + =C
y
12
c) 2x2 + 3y2 − =C
y
d) 2x2 + 3y2 + 12 ln(y) = C
24
e) 2x2 + 3y2 + =C
y
f) None of the above.
2/5
