DIFFERENTIAL EQUATIONS EXAMINATION
QUESTIONS AND CORRECT ANSWER WITH
EXPLANATION GRADED A+ STUDY GUIDE
SOUTHERN NEW HAMPSHIRE UNIVERSITY
1. A differential equation is an equation involving:
A. Derivatives
B. Only numbers
C. Only constants
D. Only matrices
Answer: A
Rationale: It contains derivatives of functions.
2. The order of a differential equation is:
A. Highest derivative present
B. Lowest derivative
C. Number of variables
D. Degree of polynomial only
Answer: A
Rationale: Based on highest derivative.
3. A first-order differential equation contains:
A. First derivative only
B. Second derivative
C. No derivatives
D. Only constants
Answer: A
Rationale: Highest derivative is first order.
4. A solution to a differential equation is:
A. A function
B. A number
C. A matrix
D. A graph only
Answer: A
Rationale: Function satisfying the equation.
,5. A general solution contains:
A. Arbitrary constants
B. No constants
C. Only numbers
D. Only graphs
Answer: A
Rationale: Family of solutions.
6. A particular solution is:
A. Specific solution with constants found
B. General form
C. Random function
D. Graph only
Answer: A
Rationale: Constants determined.
7. Initial value problem includes:
A. Condition at a point
B. No conditions
C. Graph only
D. Matrix only
Answer: A
Rationale: Starting value given.
8. Separable differential equation can be written as:
A. g(y)dy = f(x)dx
B. dy/dx = x + y
C. dy = dx only
D. f(x,y)=0
Answer: A
Rationale: Variables separated.
9. Separation of variables is used to:
A. Solve DEs
B. Multiply matrices
C. Graph only
D. Integrate only constants
Answer: A
Rationale: Integration after separation.
, 10. Linear differential equation has form:
A. dy/dx + P(x)y = Q(x)
B. y² + x = 0
C. xy = 1
D. nonlinear only
Answer: A
Rationale: Standard linear form.
11. Integrating factor is used to:
A. Solve linear DEs
B. Solve algebra
C. Graph functions
D. Multiply matrices
Answer: A
Rationale: Makes equation exact.
12. Integrating factor is usually:
A. e^(∫P(x)dx)
B. x²
C. constant
D. derivative
Answer: A
Rationale: Standard formula.
13. Exact differential equation satisfies:
A. ∂M/∂y = ∂N/∂x
B. M + N = 0
C. M = N always
D. M × N = 0
Answer: A
Rationale: Equality condition.
14. Homogeneous differential equation depends on:
A. y/x
B. x only
C. y only
D. constants only
Answer: A
Rationale: Ratio substitution.
QUESTIONS AND CORRECT ANSWER WITH
EXPLANATION GRADED A+ STUDY GUIDE
SOUTHERN NEW HAMPSHIRE UNIVERSITY
1. A differential equation is an equation involving:
A. Derivatives
B. Only numbers
C. Only constants
D. Only matrices
Answer: A
Rationale: It contains derivatives of functions.
2. The order of a differential equation is:
A. Highest derivative present
B. Lowest derivative
C. Number of variables
D. Degree of polynomial only
Answer: A
Rationale: Based on highest derivative.
3. A first-order differential equation contains:
A. First derivative only
B. Second derivative
C. No derivatives
D. Only constants
Answer: A
Rationale: Highest derivative is first order.
4. A solution to a differential equation is:
A. A function
B. A number
C. A matrix
D. A graph only
Answer: A
Rationale: Function satisfying the equation.
,5. A general solution contains:
A. Arbitrary constants
B. No constants
C. Only numbers
D. Only graphs
Answer: A
Rationale: Family of solutions.
6. A particular solution is:
A. Specific solution with constants found
B. General form
C. Random function
D. Graph only
Answer: A
Rationale: Constants determined.
7. Initial value problem includes:
A. Condition at a point
B. No conditions
C. Graph only
D. Matrix only
Answer: A
Rationale: Starting value given.
8. Separable differential equation can be written as:
A. g(y)dy = f(x)dx
B. dy/dx = x + y
C. dy = dx only
D. f(x,y)=0
Answer: A
Rationale: Variables separated.
9. Separation of variables is used to:
A. Solve DEs
B. Multiply matrices
C. Graph only
D. Integrate only constants
Answer: A
Rationale: Integration after separation.
, 10. Linear differential equation has form:
A. dy/dx + P(x)y = Q(x)
B. y² + x = 0
C. xy = 1
D. nonlinear only
Answer: A
Rationale: Standard linear form.
11. Integrating factor is used to:
A. Solve linear DEs
B. Solve algebra
C. Graph functions
D. Multiply matrices
Answer: A
Rationale: Makes equation exact.
12. Integrating factor is usually:
A. e^(∫P(x)dx)
B. x²
C. constant
D. derivative
Answer: A
Rationale: Standard formula.
13. Exact differential equation satisfies:
A. ∂M/∂y = ∂N/∂x
B. M + N = 0
C. M = N always
D. M × N = 0
Answer: A
Rationale: Equality condition.
14. Homogeneous differential equation depends on:
A. y/x
B. x only
C. y only
D. constants only
Answer: A
Rationale: Ratio substitution.
