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Differential Equation Qns

# Differential Equation Qns

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05/03/2013

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1
: E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439
1.
y = 4 sin

3x is a solution of thedifferential equation :(A)
dydx

+

8y = 0 (B)
dydx

8y = 0(C)
dydx
22

+

9y = 0 (D)
dydx
22

9y = 0
2.
The solution of the diff. equation,3 e
x
tan

y dx

+

(1

e
x
) sec
2
y dy = 0 is :(A) tan

y = c

(1

-

e
x
)
3
(B) (1 - e
x
)
3
tan

y = c(C) tan y = c (1 - e
x
)(D) (1 - e
x
) tan y = c
3.
The differential equation whosesolution is, y = A sin x + B cos x, is :(A)
dydx
22

+

y = 0 (B)
dydx
22

-

y = 0(C)
dydx

+

y = 0 (D) None of these
4.
The solution of the diff. equation,x cos y dy = (x e
x
log x + e
x
) dx, is :(A) sin y =
1x

e
x
+ c(B) sin y = e
x
log x + c = 0(C) sin y = e
x
log x + c(D) None of these
5.
The differential equation of the familyof curves, y = a cos (x + b), is :(A)
dydx
22

-

y = 0 (B)
dydx
22

+

y = 0(C)dydx
22

+

2y = 0 (D) None of these
6.
The equation of the curve whichpasses through the point (1, 1) andwhose slope is given by,
2yx
, is :(A) y = x
2
(B) x
2
- y
2
= 0(C) 2x
2
+

y
2
= 3(D) None of these
7.
The order & degree of the differentialequationdydxdydx
4- 7x = 0, are :(A) 1 &
12
(B) 2 & 1(C) 1 & 1(D) 1 & 2
8.
The differential equation for all thestraight lines which are at a unitdistance from the origin, is :(A)
yxdydx
   
2
= 1 -
dydx
   
2
(B)yxdydx
+
   
2
= 1 +dydx
   
2
(C)
yxdydx
   
2
= 1 +
dydx
   
2
(D)
yxdydx
+
   
2
= 1 -
dydx
   
2
9.
An integrating factor for thedifferential equation,(1

+

y)
2
dx
(tan

1
y
x) dy = 0, is :(A) tan
-1
y(B)
e
ytan
1
(C)
11
2
+
y
(D)
( )
11
2
xy
+
10.
The solution of the differentialequation,
dydxxx
++
1
2
= 0, is :
Differential Equations
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2
: E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439
(A) y = -
12
tan
-1
x + c(B) y + log x +x
2
2+ c = 0(C) y =
12
tan
-1
x + c(D) y - log x -
x
2
2
= c
11.
The diff. equation corresponding toprimitive, y = e
cx
, is :
OR
The elimination of the arbitraryconstant m from the equation, y = e
mx
gives the differential equation,(A)
dydx
=yx
   

log x(B)
dydx
=
xy
   

log y(C)
dydx
=
yx
   

log y(D)
dydx
=
xy
   

log x
12.
The differential equation whosesolution is, y = c
1
cos ax + c
2
sin ax is(where c
1
, c
2
are arbitrary constants)(A)
dydx
22

+

y
2
= 0 (B)
dydx
22

+

a
2
y = 0(C)
dydx
22

+

ay
2
= 0 (D)
dydx
22

a
2
y = 0
13.
The solution of differential equation
dydx
= 1 + x + y + xy, is :(A) log (1 + y) = x +x
2
2+ c(B) (1 + y)
2
= x +
x
2
2
+ c(C) log (1

+

y) = log (1

+

x) + c(D) None of these
14.
The solution of the equation,
dydx
=
()()11
+
xyyx
is :(A) log xy + x + y = c(B) log
xy
   
+ x - y = c(C) log xy + x - y = c(D) None of these
15.
The solution of differential equation,x

dydx
= y

(log y - log x + 1) is :(A) y = xe
cx
(B) y + xe
cx
= 0(C) y + e
x
= 0(D) None of these
16.
The solution of the equation,dydx= y (e
x
+ 1), is :(A) y +
( )
e
e x c
x
+ +
= 0(B) log y = e
x
+ x + c(C) log y + e
x
= x + c(D) None of these
17.
The solution of differential equation,dydxyx
++
1212coscos= 0, is :(A) tan

y + cot

x = c(B) tan

y . cot

x = c
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3
: E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439
(C) tan

y - cot

x = c(D) None of these
18.
The solution of differential equation,x

(e
2y
- 1) dy + (x
2
- 1) e
y
dx = 0, is(A) e
y
+ e
-y
= log x -
x
2
2
+ c(B) e
y
- e
-y
= log x -x
2
2+ c(C) e
y
+ e
-y
= log x +
x
2
2
+ c(D) None of these
19.
The solution of,dydx=exxyy
x
()
sinsin(log)
2
221
++
is :(A) y
2
(log y) - e
x
sin
2
x + c = 0(B) y
2
(log y) - e
x
cos
2
x + c = 0(C) y
2
(log y) + e
x
cos
2
x + c = 0(D) None of these
20.
The solution of the equation,
dydx
=
xyxy
+
, is :(A) c (x
2
+

y
2
)
1/2
+
e
yxtan(/)
1
= 0(B) c (x
2
+ y
2
)
1/2
=
e
yxtan(/)
1
(C) c (x
2
- y
2
) =
e
yxtan(/)
1
(D) None of these
21.
The solution of the equation,x

dydx
= y
x tan

yx
   
is :(A) x sin

xy
   
+ c = 0(B) x sin y + c = 0(C) x sin

yx
   
= c(D) None of these
22.
The general solution of the diff.equation, log

dydx
   
= x + y, is :(A) e
x
+ e
y
= c (B) e
x
+ e
-y
= c(C) e
-x
+ e
y
= c (D) e
-x
+ e
-y
= c
23.
The diff. equation of all straight linespassing through the point (1, -

1), is(A) y = (x

+

1)dydx

+

1(B) y = (x

+

1)dydx

1(C) y = (x

-

1)dydx

+

1(D) y = (x

-

1)dydx

-

1
24.
Equation of curve through point(1,

0) which satisfies the diff. equation(1 + y
2
)

dx - xy dy = 0, is :(A) x
2
+

y
2
= 1 (B) x
2
-

y
2
= 1(C) 2x
2
+

y
2
= 2 (D) None of these
25.
Equation of curve passing through(3,

9) which satisfies the diff. equationdydx= x +1
2
x, is :(A) 6

xy = 3x
2
- 6x + 29(B) 6xy = 3x
2
- 29x + 6(C) 6xy = 3x
2
+ 29x - 6(D) None of these
26.
The differential equation of the familyof curves, y = Ae
2x
+ Be
5x
, whereA & B are arbitrary constants, is :
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