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Byju's Answer
Standard XII
Mathematics
Differential Equations Definition
dy/dx + y/x l...
Question
d
y
d
x
+
y
x
ln
y
=
y
x
2
(
ln
y
)
2
Solving it gives
x
=
ln
y
(
c
x
2
+
1
k
)
Find
5
k
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Solution
d
y
d
x
+
y
x
ln
y
=
y
x
2
(
ln
y
)
2
Solving it gives
x
=
ln
y
(
c
x
2
+
1
k
)
−
−
−
−
−
1
Find 5k?
Use: Linear DIFFERENTIAL form
Divide by
y
(
ln
y
)
2
to whole equation
1
y
(
ln
y
)
2
d
y
d
x
+
1
x
ln
y
=
1
x
2
Put
1
ln
y
=
t
−
1
y
(
ln
y
)
2
d
y
d
x
=
d
t
d
x
d
t
d
x
−
t
x
=
−
1
x
2
I.F
=
e
∫
P
(
x
)
d
x
=
e
∫
−
1
x
d
x
=
e
−
∫
1
x
d
x
=
e
ln
1
x
I.F
=
1
x
y
(
I
.
F
)
=
∫
Q
(
x
)
.
(
I
.
F
)
d
x
+
C
Here y variable is t
t
x
=
∫
−
1
x
2
1
x
d
x
+
C
1
x
(
ln
y
)
=
1
2
x
2
+
C
1
x
=
ln
y
(
1
+
2
c
x
2
2
x
2
)
x
=
ln
y
(
c
1
x
2
+
1
2
)
−
−
−
−
−
−
2
from
1
and
2
k
=
2
5
k
=
10
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0
Similar questions
Q.
If x = e
s
i
n
3
t
, y = e
c
o
s
3
t
, show that
d
y
d
x
=
−
y
ln
x
x
ln
y
Q.
(
x
2
+
y
2
)
d
y
d
x
=
x
y
.
Solving this we get
k
y
=
e
x
r
m
y
k
+
1
.Find
r
+
m
+
k
?
Q.
sin
x
d
y
d
x
+
3
y
=
cos
x
, solving it gives
(
1
3
+
y
)
tan
k
x
2
=
c
+
2
tan
x
2
−
x
What is the value of k?
Q.
d
y
d
x
=
x
2
+
x
y
x
2
+
y
2
Solving this gives
c
(
x
−
y
)
2
/
3
(
x
3
+
x
y
+
y
3
)
1
/
5
=
[
1
√
k
t
a
n
−
1
x
+
2
y
x
√
k
]
where
e
x
p
(
x
)
=
e
x
, then what is k?
Q.
Solve:
(
x
−
y
)
d
y
=
(
x
+
y
+
1
)
d
x
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