MCQs Ordinary Differential Equations

Engineering Mathematics-II KAS203T
Compiled By: Dr. Deepa Chauhan
Multiple Choice Questions
Unit- I
Ordinary Differential Equations of Higher Order
Q.
No.
Question Options Answer
1
Roots of the auxiliary equation of the
differential equation
t
e
y
dt
dy
dt
y
d 3
2
2
4
9
6 


a)  
2
,
3
b
b)  
3
,
3
c)  
3
,
2
d)  
2
,
2
2
Particular integral of
  x
y
D
D 2
sin
4
4
2



a) 8
/
2
cos x
a
b) 4
/
2
cos x
c) 8
/
cosx
d) x
cos
3
General solution of
 
dt
d
D
y
D 

 ;
0
1
2 2
a)   2
/
2
1
t
e
tc
c
y 


d
b) 2
/
1
t
e
c
y 
c)   2
/
2
1
t
e
tc
c
y 

d)   2
/
2
1
t
e
tc
c
y 

4 Particular integral of 2
2
2
x
y
dx
y
d


a)  
2
2

x
c
b)  
2
2

x
c)  
2
2

 x
d)  
3
2

 x
5
Particular integral   ax
y
a
D sin
2
2


a) x
a
x
cos
2

a
b) x
a
x
cos
2

c) x
a
x
sin
2

d) x
a
x
cot
2

6
The order and degree of the differential
equation 0
6
8
2
4
3
3
















dx
dy
x
dx
y
d
a) (3,5)
d
b) (4, 3)
c) (4, 5)
d) (3, 4)
7 Solution of 0
2
2
2
3
3



dx
dy
dx
y
d
dx
y
d
a) 0,-1,-1
a
b) 0, 1, 1
c) 0, 0, 1
d) 1, 1, 1
8
The order and degree of the differential
equation 0
1
3
2
2









dx
dy
dx
y
d
a) (3, 2)
b
b) (2, 2)
c) (2, 5)
d) (3, 4)
9
Particular integral of
  )
(
'
'
2
x
f
e
y
D x

 

a) )
(x
f
e x

a
b) )
(x
f
e x


c) )
(
' x
f
e x

d) )
(x
f
ex
10
The differential equation whose set of
independent solution is  
x
x
x
e
x
xe
e 2
,
,
a) 0
'
3
'
'
3
'
'
' 


 y
y
y
y
d
b) 0
'
3
'
'
3
'
'
' 


 y
y
y
y
c) 0
'
3
'
'
3
'
'
' 


 y
y
y
y
d) 0
'
3
'
'
3
'
'
' 


 y
y
y
y
11
P.I. of x
y
dx
y
d
2
sin
4
2
2


a) x
x 2
cos

c
b) 4
/
x

c) 4
/
2
cos x
x

d) 4
/
2
cos x
x

12
Solve
0
,
1
,
0
)
0
(
;
tan
sec2
2
2



 x
dx
dy
y
y
y
dx
y
d
a) x
y 1
cos

b
b) x
y 1
sin

c) x
y 1
tan

d) x
y 1
sec

13
Form a differential equation if its
general solution is x
a
y sin

a) x
y
dx
dy
cot

a
b) x
y
dx
dy
cot


c) x
dx
dy
cot

d) y
dx
dy

14 P.I. of 0
2
2
2
3
3



dx
dy
dx
y
d
dx
y
d
a) 0
a
b) x
e
c) x
sin
d) x
cos
15
Form a differential equation if its
general solution is x
x
Be
Ae
y 


a) 0
2
2

 y
dx
y
d
b
b) 0
2
2

 y
dx
y
d
c) 0
2
2
2

 y
dx
y
d
d) 0
2
2
2

 y
dx
y
d
16
Solve   2
2
/
,
1
)
0
(
;
0
2
2



 
y
y
y
dx
y
d
a) x
x
y sin
3
cos 

C
b) x
x
y sin
3
cos 

c) x
x
y sin
2
cos 

d) x
x
y sin
2
cos 


17
Degree of equation
3
2
2
2
1 















dx
dy
dx
y
d
is
a) 2
a
b) 4
c) 6
d) 1
18
P.I. of   x
e
y
D
D 2
2
3
4
4 


a) 1/19
c
b)1 /20
c)1/21
d)1/22
19
Method of Variation of Parameters
a)  

 2
1
1
c
dx
v
u
uv
u
R
B
a
b)  


 2
1
1
c
dx
v
u
uv
u
R
B
c)  


 2
1
1
c
dx
v
u
uv
u
R
B
d)  

 2
1
1
c
dx
v
u
uv
u
R
B
20 Normal form is given by
a) S
Iv
dx
v
d


2
2
b
b) S
Iv
dx
v
d


2
2
c) S
v
dx
v
d


2
2
d) 0
2
2


 S
Iv
dx
v
d
21 Solve 0

 dx
y
dy
x
a) cx
y 
a
b) 0

 cx
y
c) cx
y 
d)  2
cx
y 
22
By Changing the Independent Variable
a) Q
dx
dz







2
a

b) Q
dx
dz







3
c) Q
dx
dz








2
d) Q
dx
dz








3
23 Q
y
D
f 
)
( then P.I. is
a) P
D
f
I
P
)
(
'
1
.
. 
d
b) P
D
f
I
P
)
(
1
.
. 
c) Q
D
f
I
P
)
(
'
1
.
. 
d) Q
D
f
I
P
)
(
1
.
. 
24
Homogeneous Linear Differential
Equations can be reduce to linear
differential equations with constant
coefficients by the substitution
a) x
e
z 
b
b) z
e
x 
c) z
e
x 

d) z
e
x log

25
By variation of parameters, complete
solution of given differential equation is
given by
a)
c
b)
c)
d)
26
In Solution by Changing the
Independent Variable, We choose z
such that
a) (dz/dx)2=-Q
b) (dz/dx)2=Q
c) (dz/dx)=Q
d) (dz/dx)3=Q

27 Which statement is wrong
a) 



 dx
Q
e
e
Q
D
I
P x
x 


1
.
.
b) ax
ax
e
a
f
e
D
f
I
P
)
(
1
)
(
1
.
. 

c) 



 dx
Q
e
e
Q
D
I
P x
x 


1
.
.
d) None
d
28
Equation x
e
y
dx
dy
x
dx
y
d
x 

 2
4
2
2
2
is called
a) Linear differential
equation
b) Ordinary linear
differential
equation
c) Cauchy’s
homogeneous
linear differential
equation of nth
order.
d)
Legendre’s Linear
Differential
Equation
c
29
Equation
is called
a) Linear differential
equation
b) Ordinary linear
differential
equation
c) Cauchy’s
homogeneous
linear differential
equation of nth
order.
d)
Legendre’s Linear
d

Differential
Equation
30
Linear Differential Equation of Second
Order can be solve by
a) Variation of parameters
b) By changing dependent variable
c) By changing independent
variables
d) All
d
31 If then in method of
variation of parameters. a)
b)
c)
d)
c
32
x
x
x
y
dx
dy
x
dx
y
d 3
2
2
2
cos
cos
sin
cot
.
3 



,
choose z such that
a)
c
b)
c)
d)
33 In equation, choose z such that a)
b)
c)
d)
d

34 Normal form is given by a)
b)
c)
d)
c
35 Integrating Factor of the differential
equation
a) x3
b) x2
c) x
d) 1
36 The PI of the equation a. x/2a. sinax
b. – x/2a. cosax
c. – x/2a. sinax
d. x/2a. cosax
d
37 The general solution or complete solution
of a differential equation is the solution in
which the number of
a) Particular integral is equal to the
order of differential equation
b) Complementary function is equal
to
the order of differential equation
c) Arbitrary constants is equal to the
degree of differential equation
d) Arbitrary constants is equal to the
order of differential equation
38 is the general
solution of the differential equation of
order
a) 3
b) 2
c) 1
d) 0

39
The general form of a linear differential
equation of the first order is
c)
c
40 For   0
3
5

 y
D
D d
41 P.I. of a)
b)
c)
d)
c
42 Solution of of a)
b)
c)
d)
c
43 Solution of a) a

b)
c)
d)
44. P.I. of a)
b)
c)
d)
b
45. Value of P.I. a)
b)
c)
d)
d
46.
Degree of
2
2
2
/
3
2
1
dx
y
d
dx
dy



















4
3
2
1
2
47 If the differential equation
has two equal roots then the values
of are
a)
b)
c)
d)
48 If , then I= e)
49 Value of A by variation of parameters in
y c sec
a)
b)
c)
d)
d

50 In , we can
choose Q as
a)
b)
c)
d)
c
51 Normal form Method is applicable to solve
second order ODE, if
a)
b)
c) Both
d) none
c
52 y
x
dt
dy
y
x
dt
dx
3
5
;
2
3 


 a)
b)
c)
d)
a
53 ODE of
x
x
y
dx
dy
x
dx
y
d
x
dx
y
d
x 



 log
3 2
2
2
3
3
3
a)
b)
c)
d)
c

MCQs Ordinary Differential Equations

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