Differential Equations Test

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Differential Equations Test - 4

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Question 1
1 / -0.25

Differential equations are equations containing functions y = f(x), g(x) and

A
tangent of y at zero

B
maxima of y

C
derivatives of y

D
minima of y

Solution

Differential equations are equations containing functions y = f(x), g(x) and derivatives of y with respect to x.
Question 2
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General solution of a given differential equation

A
contains arbitrary constants depending on the order of the differential equation

B
contains exactly one arbitrary constant

C
contains exactly two arbitrary constants

D
does not contain arbitrary constants

Solution

General solution of a given differential equation contains arbitrary constants depending on the order of the differential equation.
Question 3
1 / -0.25

Find a particular solution of cos

A

B

C

D

Solution
Question 4
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Differential equation of the family of circles touching the y-axis at origin is

A
2y ′ − x² = y²

B
2xyy ′ + x² = y²

C
2xyy ′ − x² = y²

D
2yy ′ + x2 = y²

Solution
Question 5
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Which of the following is a homogeneous differential equation?

A
(xy) dx − (x³ + y³ ) dy = 0

B
(x³ + 2y² ) dx + 2xy dy = 0

C
y² dx + (x² − xy − y² ) dy = 0

D
(4x + 6y + 5) dy − (3y + 2x + 4) dx = 0

Solution

y² dx + (x² − xy − y² ) dy = 0 is a homogeneous differential equation ,because the degree of each individual term is same i.e. 2.
Question 6
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Order of a differential equation is defined as

A
the number of constant terms

B
the order of the lowest order derivative ofthe dependent variable

C
the order of the highest order derivative ofthe dependent variable

D
the number of derivative terms

Solution

Order of a differential equation is defined asthe order of the highest order derivative ofthe dependent variable.
Question 7
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Particular solution of a given differential equation

A
can contain exactly one arbitrary constant

B
does not contain arbitrary constants

C
can contain exactly two arbitrary constants

D
can contain arbitrary constants

Solution

Particular solution of a given differential equationdoes not contain arbitrary constants i.e. a,b ,c etc.
Question 8
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Find a particular solution of = y tanx; y = 1 when x = 0

A
y = sec x

B
y = tan x

C
y = sin x

D
y = cos x

Solution
Question 9
1 / -0.25

Differential equation of the family of parabolas having vertex at origin and axis along positive y-axis is

A
xy ′–2y = 0

B
xy ′+ 2y = 0

C
y ′–2y = 0

D
xy ′² + 2y = 0

Solution
Question 10
1 / -0.25

A first order linear differential equation. Is a differential equation of the form

A
+ Py = Q

B
+ Py = 0

C
+ Px = Q

D
= Q

Solution

A first order linear differential equation. Is a differential equation of the form + Py = Q or + Px = Q