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Byju's Answer
Standard XII
Mathematics
Homogeneous Differential Equation
Solution of t...
Question
Solution of the differential equation
x
c
o
s
x
(
d
y
d
x
)
+
y
(
x
s
i
n
x
+
c
o
s
x
)
=
1
is
A
xy = sin x +c cos x
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B
xy sec x = tan x + C
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C
xy + sin x + c cos x = 0
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D
None of these
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Solution
The correct options are
A
xy = sin x +c cos x
B
xy sec x = tan x + C
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1
Similar questions
Q.
Solution of the differential equation
d
y
d
x
+
y
x
= sin x is
(a) x (y + cos x) = sin x + C
(b) x (y − cos x) = sin x + C
(c) x (y + cos x) = cos x + C
(d) none of these
Q.
The general solution of the differential equation
d
y
d
x
+
y
cot
x
=
sec
x
is
Q.
For the differential equation
tan
y
d
y
d
x
+
tan
x
=
cos
y
cos
3
x
.
Its solution is
sec
x
sec
y
=
x
A
+
1
B
sin
2
x
+
c
.
Find B/A?
Q.
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
Q.
Match the elements of list I, which have differential equations, with elements of list II, which have solutions of differential equations:
List I
List II
A)
y
y
1
=
sec
2
x
1)
y
sec
2
x
=
sec
x
+
c
B)
y
1
=
x
sec
y
2)
x
y
=
cos
y
+
c
C)
y
1
+
(
2
y
tan
x
)
=
sin
x
3)
x
y
=
sin
x
+
c
D)
x
y
1
+
y
=
cos
x
4)
y
2
=
2
tan
x
+
c
5)
x
2
=
2
sin
y
+
c
Then, the correct order for
A
B
C
D
is:
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