Differential Equations/Advanced Engineering Math Elements

Question 1

The solution of the differential equation 𝑥𝑑𝑦 – 𝑦𝑑𝑥 represents
which of the following?

A. Straight line passing through the origin
B. Parabola whose vertex is at the origin
C. Circle with center at the origin
D. Rectangular hyperbola

Answer 1

A

Question 2

If the roots of an equation are zero, then the solution is called:

A. Extraneous solution C. Conditional solutions
B. Trivial solutions D. Ambiguous solutions

Answer 2

B

Question 3

Equations whose members are equal only for certain or possibly
no value of the unknown.

A. Conditional equation C. Equivalent equation
B. Identical equation D. Inequalities

Answer 3

A

Question 4

A differential equation 𝑓(𝑦) 𝑑𝑦/𝑑𝑥 = 𝑔(𝑥) where f is a function of y only and g is a function of x only can be solved by:

A. Direct integration C. Homogeneous solution
B. Separation of variable D. Euler’s multiplier

Answer 4

B

Question 5

If the unknown function depends on two or more independent
variables, the differential equation is:

A. Ordinary differential equation
B. Composite differential equation
C. Compound differential equation
D. Partial differential equation

Answer 5

D

Question 6

When an equation involves one or more derivatives with respect
to a particular variable, then the variable is called:

A. Dependent variable C. Independent variable
B. Parameter D. Function

Answer 6

C

Question 6

In order for a system of n + 1 linear equations in n unknowns the
determinant formed from the coefficients of the unknowns and
the terms free of the unknowns must vanish. The determinant
formed is called of the arbitrary constants.

A. Eliminant C. Identity
B. Multiplier solution D. None of these

Answer 6

A

Question 7

If the unknown function depends only on one independent
variable, the differential equation is:

A. Ordinary differential equation
B. Partial differential equation
C. Single differential equation
D. Complete differential equation

Answer 7

A

Question 8

What does the term “homogeneous” in a differential equation
means?

A. It means that the right-hand member of a linear differential
equation is 0.
B. It means that the right-hand member of a linear differential
equation is not zero.
C. It means that the right-hand member of a linear differential
equation is the same as the left-hand member.
D. It means that both the left-hand member and the right-hand
member are 0.

Answer 8

A

Question 8

The degree of a polynomial of equation is the

A.Maximum sum of exponents
B. Maximum exponent of the variable involved
C. Exponent of the first variable
D. Exponent of the variable

Answer 8

A

Question 9

The integrating factor of the differential equation 𝑦𝑑𝑥 − 𝑥𝑑𝑦 = 0
is:

A. 𝑦2
C. 𝑥2
B. 1/𝑦2
D. 1/𝑥2

Answer 9

B

Question 10

The differential equation 𝑦′ − 𝑥𝑦 − 𝑥2 = 0 is
A. Variable separable D.E C. Un exact D.E
B. Exact D.E D. Homogeneous D.E

Answer 10

C

Question 11

A function 𝑓 (𝑥, 𝑦) is called a homogeneous function of nth
degree if

A. 𝑓 (𝑥, 𝑦) = 𝑓^𝑛 (𝑥, 𝑦) C. 𝑓 (𝑡𝑥, 𝑡𝑦) = 𝑡^𝑛 𝑓 (𝑥, 𝑦)
B. 𝑓 (𝑡𝑥, 𝑡𝑦) = 𝑡^𝑛 𝑓^𝑛 (𝑥, 𝑦) D. 𝑓𝑡^𝑛 (𝑥, 𝑦) = 𝑡^𝑛 𝑓^𝑛 (𝑥, 𝑦)

Answer 11

C

Question 12

Which of the following equations is correct?
A. All exact equations are separable equations
B. All separable equations are exact equations
C. All linear differential equations are homogenous equations
D. All homogenous equations are linear differential equations

Answer 12

B

Question 13

If equal spheres are piled in the form of a complete pyramid with
an equilateral triangle as a base. Find the number of spheres in a
pile if each side contains four spheres.
A. 20 C. 30
B. 40 D. 60

Answer 13

A

Question 14

A method of integrating a function of one variable by expressing it
as simple or more easily integrated function of another variable.

A. Integration by substitution
B. Integration by parts
C. Integration by rational fraction
D. Indefinite integration

Answer 14

A

Question 15

It is a differential equation of the form: 𝑦′ = 𝑓(𝑥) + 𝑔(𝑥)𝑦 + ℎ(𝑥)𝑦2

A. Riccati equation C. Linear differential equation
B. Bernoulli equation D. Macnay equation

Answer 15

A

Question 16

A family of curves whose equation area the solutions of a given
differential equation.

A. Integral curves C. Trigonometric curves
B. Differential curves D. Algebraic curves

Answer 16

A

Question 17

What does the term “homogeneous” in a differential equation
means?
A. It means that the right-hand member of a linear differential
equation is 0.
B. It means that the right-hand member of a linear differential
equation is not zero.
C. It means that the right-hand member of a linear differential
equation is the same as the left-hand member.
D. It means that both the left-hand member and the right-hand
member are 0.

Answer 17

A

Question 18

The process of the continuous summing of change in a function,
𝑓(𝑥) over an internal of the variable x is:
A. Differentiation C. Summation
B. Integration D. Interval addition

Answer 18

A