MATH 2660
DIFFERENTIAL EQUATIONS
COMPREHENSIVE PREP
Exam-Style Practice Questions & Problems
Correct Answers · Rationales · Step Guidance
FIRST-ORDER · SECOND-ORDER · SYSTEMS · APPLICATIONS
HIGH-QUALITY · EXAM-READY
Integrating Factors · Separable · Characteristic Equations
Undetermined Coefficients · Eigenvalue Method · Models
QUICK · CLEAR · PROFESSIONAL
,MATH 2660 | DIFFERENTIAL EQUATIONS | COMPREHENSIVE PREP Exam Practice
PRACTICE SET 1
1. The integrating factor for y' + (1)y = x is:
A. e^{1 x}
B. e^{-1 x}
C. e^x
D. 1
Correct Answer: A
Rationale:
mu = exp(integral 1 dx).
Multiply and integrate.
2. The integrating factor for y' + (2)y = x is:
A. e^{2 x}
B. e^{-2 x}
C. e^x
D. 2
Correct Answer: A
Rationale:
mu = exp(integral 2 dx).
Multiply and integrate.
3. The integrating factor for y' + (3)y = x is:
A. e^{3 x}
B. e^{-3 x}
C. e^x
D. 3
Correct Answer: A
Rationale:
mu = exp(integral 3 dx).
Multiply and integrate.
4. The integrating factor for y' + (4)y = x is:
A. e^{4 x}
B. e^{-4 x}
C. e^x
D. 4
Correct Answer: A
Rationale:
mu = exp(integral 4 dx).
Multiply and integrate.
Page 2
,MATH 2660 | DIFFERENTIAL EQUATIONS | COMPREHENSIVE PREP Exam Practice
PRACTICE SET 2
5. The integrating factor for y' + (5)y = x is:
A. e^{5 x}
B. e^{-5 x}
C. e^x
D. 5
Correct Answer: A
Rationale:
mu = exp(integral 5 dx).
Multiply and integrate.
6. The integrating factor for y' + (6)y = x is:
A. e^{6 x}
B. e^{-6 x}
C. e^x
D. 6
Correct Answer: A
Rationale:
mu = exp(integral 6 dx).
Multiply and integrate.
7. The integrating factor for y' + (7)y = x is:
A. e^{7 x}
B. e^{-7 x}
C. e^x
D. 7
Correct Answer: A
Rationale:
mu = exp(integral 7 dx).
Multiply and integrate.
8. The integrating factor for y' + (8)y = x is:
A. e^{8 x}
B. e^{-8 x}
C. e^x
D. 8
Correct Answer: A
Rationale:
mu = exp(integral 8 dx).
Multiply and integrate.
Page 3
, MATH 2660 | DIFFERENTIAL EQUATIONS | COMPREHENSIVE PREP Exam Practice
PRACTICE SET 3
9. The integrating factor for y' + (9)y = x is:
A. e^{9 x}
B. e^{-9 x}
C. e^x
D. 9
Correct Answer: A
Rationale:
mu = exp(integral 9 dx).
Multiply and integrate.
10. The integrating factor for y' + (10)y = x is:
A. e^{10 x}
B. e^{-10 x}
C. e^x
D. 10
Correct Answer: A
Rationale:
mu = exp(integral 10 dx).
Multiply and integrate.
11. For the equation y'' - 1 y' + 1 y = 0, the characteristic roots are found from:
A. r^2 - 1 r + 1 = 0
B. r + 1 = 0
C. Only r=0
D. Laplace only
Correct Answer: A
Rationale:
Standard characteristic polynomial.
Solve quadratic for r.
12. For the equation y'' - 2 y' + 2 y = 0, the characteristic roots are found from:
A. r^2 - 2 r + 2 = 0
B. r + 2 = 0
C. Only r=0
D. Laplace only
Correct Answer: A
Rationale:
Standard characteristic polynomial.
Solve quadratic for r.
Page 4
DIFFERENTIAL EQUATIONS
COMPREHENSIVE PREP
Exam-Style Practice Questions & Problems
Correct Answers · Rationales · Step Guidance
FIRST-ORDER · SECOND-ORDER · SYSTEMS · APPLICATIONS
HIGH-QUALITY · EXAM-READY
Integrating Factors · Separable · Characteristic Equations
Undetermined Coefficients · Eigenvalue Method · Models
QUICK · CLEAR · PROFESSIONAL
,MATH 2660 | DIFFERENTIAL EQUATIONS | COMPREHENSIVE PREP Exam Practice
PRACTICE SET 1
1. The integrating factor for y' + (1)y = x is:
A. e^{1 x}
B. e^{-1 x}
C. e^x
D. 1
Correct Answer: A
Rationale:
mu = exp(integral 1 dx).
Multiply and integrate.
2. The integrating factor for y' + (2)y = x is:
A. e^{2 x}
B. e^{-2 x}
C. e^x
D. 2
Correct Answer: A
Rationale:
mu = exp(integral 2 dx).
Multiply and integrate.
3. The integrating factor for y' + (3)y = x is:
A. e^{3 x}
B. e^{-3 x}
C. e^x
D. 3
Correct Answer: A
Rationale:
mu = exp(integral 3 dx).
Multiply and integrate.
4. The integrating factor for y' + (4)y = x is:
A. e^{4 x}
B. e^{-4 x}
C. e^x
D. 4
Correct Answer: A
Rationale:
mu = exp(integral 4 dx).
Multiply and integrate.
Page 2
,MATH 2660 | DIFFERENTIAL EQUATIONS | COMPREHENSIVE PREP Exam Practice
PRACTICE SET 2
5. The integrating factor for y' + (5)y = x is:
A. e^{5 x}
B. e^{-5 x}
C. e^x
D. 5
Correct Answer: A
Rationale:
mu = exp(integral 5 dx).
Multiply and integrate.
6. The integrating factor for y' + (6)y = x is:
A. e^{6 x}
B. e^{-6 x}
C. e^x
D. 6
Correct Answer: A
Rationale:
mu = exp(integral 6 dx).
Multiply and integrate.
7. The integrating factor for y' + (7)y = x is:
A. e^{7 x}
B. e^{-7 x}
C. e^x
D. 7
Correct Answer: A
Rationale:
mu = exp(integral 7 dx).
Multiply and integrate.
8. The integrating factor for y' + (8)y = x is:
A. e^{8 x}
B. e^{-8 x}
C. e^x
D. 8
Correct Answer: A
Rationale:
mu = exp(integral 8 dx).
Multiply and integrate.
Page 3
, MATH 2660 | DIFFERENTIAL EQUATIONS | COMPREHENSIVE PREP Exam Practice
PRACTICE SET 3
9. The integrating factor for y' + (9)y = x is:
A. e^{9 x}
B. e^{-9 x}
C. e^x
D. 9
Correct Answer: A
Rationale:
mu = exp(integral 9 dx).
Multiply and integrate.
10. The integrating factor for y' + (10)y = x is:
A. e^{10 x}
B. e^{-10 x}
C. e^x
D. 10
Correct Answer: A
Rationale:
mu = exp(integral 10 dx).
Multiply and integrate.
11. For the equation y'' - 1 y' + 1 y = 0, the characteristic roots are found from:
A. r^2 - 1 r + 1 = 0
B. r + 1 = 0
C. Only r=0
D. Laplace only
Correct Answer: A
Rationale:
Standard characteristic polynomial.
Solve quadratic for r.
12. For the equation y'' - 2 y' + 2 y = 0, the characteristic roots are found from:
A. r^2 - 2 r + 2 = 0
B. r + 2 = 0
C. Only r=0
D. Laplace only
Correct Answer: A
Rationale:
Standard characteristic polynomial.
Solve quadratic for r.
Page 4
