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Byju's Answer
Standard XII
Mathematics
Linear Differential Equations of First Order
Find the gene...
Question
Find the general solution of the differential equation
(
1
+
y
2
)
d
x
=
(
tan
−
1
y
−
x
)
d
y
Open in App
Solution
(
1
+
y
2
)
d
x
=
(
t
a
n
−
1
y
−
x
)
d
y
d
x
d
y
=
t
a
n
−
1
y
1
+
y
2
=
x
1
+
y
2
d
x
s
y
+
x
1
+
y
2
=
t
a
n
−
1
y
1
+
y
2
d
x
d
y
+
x
1
+
y
2
=
t
a
n
−
1
y
1
+
y
2
________ (1)
Integrating factor =
e
∫
1
1
+
y
2
d
y
=
e
t
a
n
−
1
y
now, solution of equation (1) is
x
×
I
.
F
=
∫
I
.
F
×
t
a
n
−
1
y
1
+
y
2
d
y
x
.
e
t
a
n
−
1
y
=
∫
e
t
a
n
−
1
y
t
a
n
−
1
y
1
+
y
2
d
y
_________ (2)
x
.
e
t
a
n
−
1
y
⇒
let
t
a
n
−
1
y
=
p
1
1
+
y
2
d
y
=
d
p
So RHS in equation (2) is
∫
e
t
a
n
−
1
y
.
t
a
n
−
1
y
1
+
y
2
d
y
=
∫
P
.
e
p
d
p
=
p
e
p
−
p
From equation (2)
x
e
t
a
n
−
1
y
=
t
a
n
−
1
y
e
t
a
n
−
1
y
−
t
a
n
−
1
y
+
c
x
e
t
a
n
−
1
y
=
t
a
n
−
1
y
(
e
t
a
n
−
1
y
−
1
)
+
c
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0
Similar questions
Q.
Find general solution of differential solution given below:
(
1
+
y
2
)
d
x
=
(
tan
−
1
y
−
x
)
d
y
Q.
Solution of the differential equation
(
1
+
y
2
)
d
x
=
(
1
−
t
a
n
−
1
y
−
x
)
d
y
is
Q.
Find the particular solution of the differential equation
(
t
a
n
−
1
y
−
x
)
d
y
=
(
1
+
y
2
)
d
x
, given that when
x
=
0
,
y
=
0
.
Q.
Solve differential equation
(
1
+
y
2
)
d
x
=
(
tan
−
1
y
−
x
)
d
y
.
Q.
Solve the differential equation:
(
tan
−
1
y
−
x
)
d
y
=
(
1
+
y
2
)
d
x
.
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