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Recent questions in Differential Equations
Questions
>>
CBSE XII
>>
Math
>>
Differential Equations
The number of solutions of
d
y
d
x
=
y
+
1
x
−
1
when y(1)=2 is
(
A
)
n
o
n
e
(
B
)
o
n
e
(
C
)
t
w
o
(
D
)
i
n
f
i
n
i
t
e
cbse
class12
ch9
q45
p197
objective
exemplar
sec-a
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Solution of
d
y
d
x
−
y
=
1
,
y
(
0
)
=
1
is given by
(
A
)
x
y
=
−
e
x
(
B
)
x
y
=
−
e
−
x
(
C
)
x
y
=
−
1
(
D
)
y
=
2
e
x
−
1
cbse
class12
ch9
sec-a
q44
p196
objective
exemplar
medium
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Integrating factor of
x
d
x
d
y
−
y
=
x
4
−
3
x
is
(
A
)
x
(
B
)
l
o
g
x
(
C
)
1
x
(
D
)
−
x
cbse
class12
ch9
sec-a
q43
p196
objective
exemplar
easy
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Family
y
=
A
x
+
A
3
of curves is represented by the differential equation of degree
(
A
)
1
(
B
)
2
(
C
)
3
(
D
)
4
cbse
class12
ch9
sec-a
q42
p196
objective
exemplar
easy
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Solution of the differential equation
tan
y
sec
2
x
d
x
+
tan
x
sec
2
y
d
y
=
0
is
(
A
)
tan
x
+
tan
y
=
c
(
B
)
tan
x
−
tan
y
=
c
(
C
)
tan
x
tan
y
=
c
(
D
tan
x
.
t
a
n
y
=
c
cbse
class12
ch9
sec-a
q41
p196
objective
exemplar
medium
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Integrating factor of the differential equation
cos
x
d
y
d
x
+
y
sin
x
=
1
is:
(
A
)
cos
x
(
B
)
tan
x
(
C
)
sec
x
(
D
)
sin
x
cbse
class12
ch9
sec-a
q40
p196
objective
exemplar
medium
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Solution of differential equation
x
d
y
−
y
d
x
=
0
represents:
cbse
class12
ch9
sec-a
q39
p196
objective
exemplar
easy
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
The differential equation for
y
=
A
cos
α
x
+
B
sin
α
x
,
where A and B are arbitrary constants is
(
A
)
d
2
y
d
x
2
+
x
2
y
=
0
(
B
)
d
2
y
d
x
2
+
α
2
y
=
0
(
C
)
d
2
y
d
x
2
+
y
=
0
(
D
)
d
2
y
d
x
2
−
y
=
0
cbse
class12
ch9
sec-a
q38
p196
objective
exemplar
easy
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
If
y
=
e
−
x
(
A
cos
x
+
B
sin
x
)
, then
y
is a solution of
cbse
class12
ch9
differential-equations
sec-a
q37
p195
objective
exemplar
difficult
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
The order and degree of the differential equation
d
2
y
d
x
2
+
(
d
y
d
x
)
1
4
+
x
1
5
=
0
,respectively,are
(
A
)
2
a
n
d
n
o
t
d
e
f
i
n
e
d
(
B
)
2
a
n
d
2
(
C
)
2
a
n
d
3
(
D
)
3
a
n
d
3
cbse
class12
ch9
sec-a
q36
p195
objective
exemplar
easy
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
The degree of the differential equation
1
+
[
(
d
y
d
x
)
2
]
3
2
=
d
2
y
d
x
2
is:
(
A
)
4
(
B
)
3
2
(
C
)
n
o
t
d
e
f
i
n
e
d
(
D
)
2
cbse
class12
ch9
sec-a
q35
p195
objective
exemplar
easy
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
The degree of the differential equation
(
d
2
y
d
x
2
)
2
+
(
d
y
d
x
)
2
=
x
sin
(
d
y
d
x
)
is:
(
A
)
1
(
B
)
2
(
C
)
3
(
D
)
n
o
t
d
e
f
i
n
e
d
cbse
class12
ch9
sec-a
q34
p195
objective
exemplar
easy
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Solve:
x
d
y
d
x
=
y
(
log
y
−
log
x
+
1
)
cbse
class12
ch9
sec-a
q33
p195
exemplar
medium
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Find the equation of a curve passing through the point (1,1).If the tangent drawn at any point P(x,y) on the curve meets the coordinate axes at A and B such that P is the mid-point of AB.
cbse
class12
ch9
sec-b
q32
p195
exemplar
difficult
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Find the equation of a curve passing through origin if the slope of the tangent to the curve at any point
(
x
,
y
)
is equal to the square of the difference of the abscissa and the ordinate of the point.
cbse
class12
ch9
sec-b
q31
p195
exemplar
medium
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Find the equation of the curve through the point (1,0) if the slope of the tangent to the curve at any point (x,y) is
y
−
1
x
2
+
x
.
cbse
class12
ch9
sec-b
q30
p195
exemplar
medium
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Find the equation of a curve passing through (2,1) if the slope of the tangent to the curve at any point (x,y) is
x
2
+
y
2
2
x
y
.
cbse
class12
ch9
sec-b
q29
p194
exemplar
difficult
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Find the general solution of
d
y
d
x
+
3
y
=
sin
2
x
cbse
class12
ch9
sec-b
q28
p194
exemplar
difficult
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Solve :
d
y
d
x
=
cos
(
x
+
y
)
+
sin
(
x
+
y
)
.[Hint :Substitute x+y=z]
cbse
class12
ch9
sec-b
q27
p194
exemplar
difficult
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
FInd the general solution of
(
1
+
tan
y
)
(
d
x
−
d
y
)
+
2
x
d
y
=
0
cbse
class12
ch9
sec-a
q26
p194
exemplar
difficult
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Solve:
y
+
d
d
x
(
x
y
)
=
x
(
sin
x
+
l
o
g
x
)
cbse
class12
ch9
sec-b
q25
p194
exemplar
difficult
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Find the differential equation of system of concentric circles with centre(1,2).
cbse
class12
ch9
sec-a
q24
p194
short-answer
exemplar
easy
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Solve the differential equation
(
1
+
y
2
)
tan
−
1
x
d
x
+
2
y
(
1
+
x
2
)
d
y
=
0
cbse
class12
ch9
sec-b
q23
p194
short-answer
exemplar
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Form the differential equation by eliminating A and B in
A
x
2
+
B
y
2
=
1
.
cbse
class12
ch9
sec-b
q22
p194
short-answer
exemplar
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Solve the differential equation
d
y
=
cos
x
(
2
−
y
c
o
s
e
c
x
)
d
x
given that
y
=
2
when
x
=
π
2
.
cbse
class12
ch9
sec-b
q21
p194
short-answer
exemplar
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Solve:
2
(
y
+
3
)
−
x
y
d
y
d
x
=
0
,
given that
y
(
1
)
=
−
2
cbse
class12
ch9
sec-b
q20
p194
short-answer
exemplar
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Solve:
(
x
+
y
)
(
d
x
−
d
y
)
=
d
x
+
d
y
.
[Hint:Substitute x+y=z after separating dx and dy]
cbse
class12
ch9
sec-b
q19
p194
short-answer
exemplar
difficult
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Find the general solution of
y
2
d
x
+
(
x
2
−
x
y
+
y
2
)
d
y
=
0
cbse
class12
ch9
sec-b
q18
p194
short-answer
exemplar
difficult
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Find the general solution of the differential equation
(
1
+
y
2
)
+
(
x
−
e
tan
−
1
y
)
d
y
d
x
=0
cbse
class12
ch9
sec-b
q17
p194
short-answer
exemplar
medium
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Solve:
x
2
d
y
d
x
=
x
2
+
x
y
+
y
2
cbse
class12
ch9
sec-b
q16
p194
short-answer
exemplar
medium
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Find the equation of a curve passing through origin and satisfying the differential equation
(
1
−
x
2
)
d
y
d
x
−
2
x
y
=
4
x
2
cbse
class12
ch9
sec-b
q15
p194
short-answer
exemplar
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Form the differential equation of all circles which pass through origin and whose centers lie on y-axis as shown below:
cbse
class12
ch9
sec-b
q14
p194
short-answer
exemplar
math
difficult
jeemain
differential-equations
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Form the differential equation having
y
=
(
sin
−
1
x
)
2
+
A
cos
−
1
x
+
B
,
where A and B are arbitrary constants,as its general solution.
cbse
class12
ch9
sec-b
q13
p194
short-answer
exemplar
medium
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
If y(t) is a solution of
(
1
+
t
)
d
y
d
t
−
t
y
=
1
and
y
(
0
)
=
−
1
,
then show that y(1)=
−
1
2
cbse
class12
ch9
sec-b
q12
p193
short-answer
exemplar
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
If y(x) is a solution of
2
−
sin
x
1
−
y
(
d
y
d
x
)
=
−
cos
x
and y(0)=1,then find the value of
1
2
.
cbse
class12
ch9
sec-b
q11
p193
short-answer
exemplar
medium
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Find the general solution of
(
x
+
2
y
3
)
d
y
d
x
=
y
d
x
cbse
class12
ch9
sec-b
q10
p193
short-answer
exemplar
easy
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
Solve the differential equation
d
y
d
x
=
1
+
x
+
y
2
+
x
y
2
,
when y=0,x=0.
cbse
class12
ch9
sec-b
q9
p193
short-answer
exemplar
easy
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
Solve:
y
d
x
−
x
d
y
=
x
2
y
d
x
cbse
class12
ch9
sec-a
q8
p193
short-answer
exemplar
easy
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
Solve the differential equation
d
y
d
x
+
1
=
e
x
+
y
cbse
class12
ch9
sec-a
q7
p193
short-answer
exemplar
easy
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
Find the general solution of
d
y
d
x
=
a
y
−
e
m
x
cbse
class12
ch9
sec-b
q6
p193
short-answer
exemplar
medium
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
Solve the differential equation
d
y
d
x
=
2
x
y
−
y
cbse
class12
ch9
sec-a
q5
p193
short-answer
exemplar
easy
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
Solve the differential equation
(
x
2
−
1
)
d
y
d
x
+
2
x
y
=
1
x
2
−
1
cbse
class12
ch9
sec-b
q4
p193
short-answer
exemplar
medium
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
Given that
d
y
d
x
=
e
−
2
y
and
y
=
0
when
x
=
5
. Find the value of
x
when
y
=
3
.
cbse
class12
ch9
sec-a
q3
p193
short-answer
exemplar
medium
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
Find the differential equation of all non vertical lines in a plane.
cbse
class12
ch9
sec-a
q2
p193
short-answer
exemplar
easy
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
Find the solution of
d
y
d
x
=
2
y
−
x
.
cbse
class12
ch9
sec-a
q1
p193
short-answer
exemplar
easy
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
For the differential equations, find the particular solution satisfying the given condition:
[
x
s
i
n
2
(
x
y
−
y
)
]
d
x
+
x
d
y
=
0
;
y
π
4
w
h
e
n
x
=
1
cbse
class12
bookproblem
ch9
sec5
q13
p406
difficult
sec-b
math
asked
Dec 12, 2012
by
thanvigandhi_1
1
answer
Show that the differential equation is homogeneous and solve :
(
1
+
e
x
y
)
d
x
+
e
x
y
(
1
−
x
y
)
d
y
=
0
cbse
class12
bookproblem
ch9
sec5
q10
p406
difficult
sec-b
math
asked
Dec 12, 2012
by
thanvigandhi_1
1
answer
Verify that the given function(explicit or implicit)is a solution of the corresponding differential equation
y
=
e
x
+
1
:
y
″
−
y
′
=
0
cbse
class12
bookproblem
ch9
sec2
q1
p385
easy
sec-a
math
asked
Nov 30, 2012
by
sreemathi.v
1
answer
Verify that the given function(explicit or implicit)is a solution of the corresponding differential equation
y
=
x
2
+
2
x
+
C
:
y
′
−
2
x
−
2
=
0
cbse
class12
bookproblem
ch9
sec2
q2
p385
easy
sec-a
math
asked
Nov 30, 2012
by
sreemathi.v
1
answer
Verify that the given function(explicit or implicit)is a solution of the corresponding differential equation
y
=
cos
x
+
C
:
y
′
+
sin
x
=
0
cbse
class12
bookproblem
ch9
sec2
q3
p385
easy
sec-a
math
asked
Nov 30, 2012
by
sreemathi.v
1
answer
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